9.5 Composition of Functions

📖 Chapter 9 Combinations of Functions
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1

001. Q1a

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.linear.quad, find.fog(x)
🎓 001. Algebraic composition between linear and quadratic
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001. Q1b

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.linear.quad, find.fog(x)
🎓 001. Algebraic composition between linear and quadratic
⏱️ 0:211🎬 n3Egh1gNSbk
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3

001. Q1c

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.linear.quad, find.fog(x)
🎓 001. Algebraic composition between linear and quadratic
⏱️ 0:341🎬 766WDAzpYSs
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001. Q1d

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.linear.quad, find.fog(x)
🎓 001. Algebraic composition between linear and quadratic
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001. Q1e

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001. Q1f

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.linear.quad, find.fog(x)
🎓 001. Algebraic composition between linear and quadratic
⏱️ 0:241🎬 73QfQq1osSg
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002. Q2a

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002. Q2b

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002. Q2c

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002. Q2d

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002. Q2e

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002. Q2f

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13

003. Q3a

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📚 Related Lectures
12.6.1 AdvFun, Combined Functions, Composite Functions, given Graphs, find fog(a)
🎓 001. fog(a) given graph
⏱️ 0:230🎬 MiW8YXySCRg
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14

003. Q3b

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📚 Related Lectures
12.6.1 AdvFun, Combined Functions, Composite Functions, given Graphs, find fog(a)
🎓 001. fog(a) given graph
⏱️ 0:190🎬 sTH1koRPthE
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15

003. Q3c

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📚 Related Lectures
12.6.1 AdvFun, Combined Functions, Composite Functions, given Graphs, find fog(a)
🎓 001. fog(a) given graph
⏱️ 0:170🎬 FkM07ugHGAc
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16

003. Q3d

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📚 Related Lectures
12.6.1 AdvFun, Combined Functions, Composite Functions, given Graphs, find fog(a)
🎓 001. fog(a) given graph
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17

004. Q4

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18

005. Q5a

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Answer
📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.linear.quad, find.fog(x)
🎓 001. Algebraic composition between linear and quadratic
⏱️ 0:550🎬 _zv2-ihGoBw
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19

005. Q5b

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.quad.quad, combine
🎓 001. Combining two quadratic functions
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20

005. Q5c

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.poly.poly, combine
🎓 001. Sum of Polynomial Functions
🎓 002. Composite of polynomial functions
⏱️ 1:080🎬 iKCblIWhf2k
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21

005. Q5d

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.poly.poly, combine
🎓 001. Sum of Polynomial Functions
🎓 002. Composite of polynomial functions
⏱️ 1:580🎬 N8m_u0bCJm0
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005. Q5e

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📚 Related Lectures
12.6.1 ADVFUN, Composite Functions, given Functions, determine fog=gof
🎓 001. Comparing fog and gof
⏱️ 1:250🎬 iL0TggpvFmo
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005. Q5f

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📚 Related Lectures
12.6.1 ADVFUN, Composite Functions, given Functions, determine fog=gof
🎓 001. Comparing fog and gof
⏱️ 1:010🎬 bGQBNSrI2wo
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24

006. Q6a

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📚 Related Lectures
12.6.1 ADVFUN, Composite Functions, given Functions, determine fog=gof
🎓 001. Comparing fog and gof
⏱️ 1:460🎬 pM-RRaq4t9M
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25

006. Q6b

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📚 Related Lectures
12.6.1 ADVFUN, Composite Functions, given Functions, determine fog=gof
🎓 001. Comparing fog and gof
⏱️ 1:260🎬 6sbdIV1Mx-E
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006. Q6c

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📚 Related Lectures
12.6.1 ADVFUN, Composite Functions, given Functions, determine fog=gof
🎓 001. Comparing fog and gof
⏱️ 3:270🎬 -fujH4oIuIs
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006. Q6d

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📚 Related Lectures
12.6.1 ADVFUN, Composite Functions, given Functions, determine fog=gof
🎓 001. Comparing fog and gof
⏱️ 1:460🎬 NQcS4TPMv64
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006. Q6e

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📚 Related Lectures
12.6.1 ADVFUN, Composite Functions, given Functions, determine fog=gof
🎓 001. Comparing fog and gof
⏱️ 2:591🎬 I1fWgGR6Sa8
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006. Q6f

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📚 Related Lectures
12.6.1 ADVFUN, Composite Functions, given Functions, determine fog=gof
🎓 001. Comparing fog and gof
⏱️ 2:340🎬 1fCz0tb47Ps
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30

007. Q7a

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.fog.Polynomial, decompose.find.f.and.g
🎓 001. Decomposition
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007. Q7b

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.fog.Polynomial, decompose.find.f.and.g
🎓 001. Decomposition
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007. Q7c

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📚 Related Lectures
12.6.1 AdvFun, Composite Functions, given.Composite.Function.fog, decompose
🎓 001. Decomposition of functions
⏱️ 0:401🎬 dcQ1CohnJxA
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33

007. Q7d

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📚 Related Lectures
12.6.1 AdvFun, Composite Functions, given.Composite.Function.fog, decompose
🎓 001. Decomposition of functions
⏱️ 0:200🎬 rYAgobn039A
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007. Q7e

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.fog.Polynomial, decompose.find.f.and.g
🎓 001. Decomposition
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35

007. Q7f

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.fog.Polynomial, decompose.find.f.and.g
🎓 001. Decomposition
⏱️ 0:390🎬 eP8jqfG9jo0
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36

008. Q8a

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Answer
📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.linear.quad, find.fog(x)
🎓 001. Algebraic composition between linear and quadratic
⏱️ 0:190🎬 oaSHcybRlHw
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37

008. Q8b

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38

008. Q8c

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39

009. Q9a

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📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.linear.linear, combine
🎓 001. Quotient of Linear Functions
⏱️ 1:440🎬 Qu72eD2Ajzs
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40

009. Q9b

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Answer
📚 Related Lectures
12.6 ADVFUN, Combined Functions, given.linear.linear, find.fog
🎓 002. fogof with two linear functions
🎓 001. fog with two linear functions
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010. Q10

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011. Q11

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012. Q12

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013. Q13

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014. Q14a

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Answer
📚 Related Lectures
12.6 AdvFun, Combined Functions, given Graphs, sketch Sum
🎓 003. Subtraction of two parabolas
🎓 002. Sum of two functions visually, Curves
🎓 001. Sum of two functions visually, Straight Lines
⏱️ 1:050🎬 fLBBLH2IK3w
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014. Q14b

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Answer
📚 Related Lectures
12.6 AdvFun, Combined Functions, given Graphs, sketch Sum
🎓 003. Subtraction of two parabolas
🎓 002. Sum of two functions visually, Curves
🎓 001. Sum of two functions visually, Straight Lines
⏱️ 0:390🎬 N3ta_QOhkrg
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47

014. Q14c

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📚 Related Lectures
12.6 AdvFun, Combined Functions, given Graphs, sketch Sum
🎓 003. Subtraction of two parabolas
🎓 002. Sum of two functions visually, Curves
🎓 001. Sum of two functions visually, Straight Lines
⏱️ 0:390🎬 lin6QUPb8dM
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48

014. Q14d

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Answer
📚 Related Lectures
12.6 AdvFun, Combined Functions, given Graphs, sketch Sum
🎓 003. Subtraction of two parabolas
🎓 002. Sum of two functions visually, Curves
🎓 001. Sum of two functions visually, Straight Lines
⏱️ 0:370🎬 AdWfiEqXQik
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49

014. Q14e

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Answer
📚 Related Lectures
12.6 AdvFun, Combined Functions, given Graphs, sketch Sum
🎓 003. Subtraction of two parabolas
🎓 002. Sum of two functions visually, Curves
🎓 001. Sum of two functions visually, Straight Lines
⏱️ 1:110🎬 aT5UJEO9Jdc
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50

014. Q14f

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📚 Related Lectures
12.6 AdvFun, Combined Functions, given Graphs, sketch Sum
🎓 003. Subtraction of two parabolas
🎓 002. Sum of two functions visually, Curves
🎓 001. Sum of two functions visually, Straight Lines
⏱️ 0:490🎬 833tR3b3NDI
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51

014. Q14g

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Answer
📚 Related Lectures
12.6 AdvFun, Combined Functions, given Graphs, sketch Sum
🎓 003. Subtraction of two parabolas
🎓 002. Sum of two functions visually, Curves
🎓 001. Sum of two functions visually, Straight Lines
⏱️ 0:500🎬 BoijzUW9bL0
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52

014. Q14h

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Answer
📚 Related Lectures
12.6 AdvFun, Combined Functions, given Graphs, sketch Sum
🎓 003. Subtraction of two parabolas
🎓 002. Sum of two functions visually, Curves
🎓 001. Sum of two functions visually, Straight Lines
⏱️ 0:360🎬 I4pdd2H4Gng
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014. Q14i

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Answer
📚 Related Lectures
12.6 AdvFun, Combined Functions, given Graphs, sketch Sum
🎓 003. Subtraction of two parabolas
🎓 002. Sum of two functions visually, Curves
🎓 001. Sum of two functions visually, Straight Lines
⏱️ 0:550🎬 _8nNvGsLrOE
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54

014. Q14j

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Answer
📚 Related Lectures
12.6 AdvFun, Combined Functions, given Graphs, sketch Sum
🎓 003. Subtraction of two parabolas
🎓 002. Sum of two functions visually, Curves
🎓 001. Sum of two functions visually, Straight Lines
⏱️ 0:450🎬 HZ2veMxQjRQ
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014. Q14k

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📚 Related Lectures
12.6 AdvFun, Combined Functions, given Graphs, sketch Sum
🎓 003. Subtraction of two parabolas
🎓 002. Sum of two functions visually, Curves
🎓 001. Sum of two functions visually, Straight Lines
⏱️ 0:490🎬 aCCat647vEE
▶ Watch
56

014. Q14l

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Answer
📚 Related Lectures
12.6 AdvFun, Combined Functions, given Graphs, sketch Sum
🎓 003. Subtraction of two parabolas
🎓 002. Sum of two functions visually, Curves
🎓 001. Sum of two functions visually, Straight Lines
⏱️ 0:410🎬 SNrdI4wn9tw
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57

016. Q16a

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Answer
📚 Related Lectures
12.6 AdvFun, Combined Functions, given.three.function, find.fogoh
🎓 001. Evaluating fogoh
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016. Q16b

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Answer
📚 Related Lectures
12.6 AdvFun, Combined Functions, given.three.function, find.fogoh
🎓 001. Evaluating fogoh
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advfnsnelsonCh9.5lecturesTube

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1

001. Review of Combining functions

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002. Composition Analogy

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003. Composition with Set of Points

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004. Composition with Algegra

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5

005. Decomposition of Functions

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006. Decomposition example

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007. Decomposition example 3

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008. Triple Composition

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