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- ACCUPLACER Test Prep
- Functions
Composite functions
- Intro Lesson: a7:14
- Intro Lesson: b17:28
- Lesson: 1a3:27
- Lesson: 1b6:43
- Lesson: 1c2:58
- Lesson: 1d6:24
- Lesson: 1e7:42
- Lesson: 2a6:46
- Lesson: 2b3:38
- Lesson: 2c2:27
- Lesson: 2d2:44
- Lesson: 3a6:56
- Lesson: 3b5:38
- Lesson: 3c6:42
- Lesson: 3d5:48
- Lesson: 4a11:03
- Lesson: 4b9:04
- Lesson: 5a8:01
- Lesson: 5b6:21
- Lesson: 5c20:05
- Lesson: 6a8:01
- Lesson: 6b6:21
- Lesson: 6c20:05
Composite functions
Related Concepts: Quotient rule
Lessons
- IntroductionWhat is a "Composite Function"?a)Quick review on basic operations with functions.b)Composition of Functions: putting one function inside another function!
- 1.Introduction to Composite Functions
If f(x)=4x−5
g(x)=8x2+6
Determinea)(f∘g)(x)b)(g∘f)(x)c)(f∘f)(x)d)(g∘g)(x)e)(f∘g)(2)evaluate in two different ways - 2.Evaluate a Composite Function Graphically
Use the graphs of f(x) and g(x) to evaluate the following:
a)f(g(−4))b)f(g(0))c)g(f(−2))d)g(f(−3)) - 3.Determine the Composition of Three Functions
Use the functions f(x)=3x,g(x)=x−7and h(x)=x2
to determine each of the following:a)(f∘g∘h)(x)b)g(f(h(x)))c)f(h(g(x)))d)(h∘g∘f)(x) - 4.Determine the Original Functions From a Composite Function
If h(x)=(f∘g)(x)determine f(x)and g(x)a)h(x)=(7x−5)3−4(7x−5)+1b)h(x)=4x3−9, give two possible sets of solutions - 5.Composite Functions with Restrictions
Consider f(x)=x−13and g(x)=x2+4, for each of the function below:a)Determine:
i) (f∘g)(x)
ii) (g∘f)(x)b)State the domain and range of:
i) f(x)
ii) g(x)
iii) (f∘g)(x)
iv) (g∘f)(x)c)Sketch the graph of:
i) f(x)
ii) g(x)
iii) (f∘g)(x)
iv) (g∘f)(x) - 6.Composite Functions with Restrictions
Consider f(x)=x−13and g(x)=x2+4, for each of the function below:
i) state the domain and range
ii) sketch the graph.a)f(x)b)g(x)c)(f∘g)(x)
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40.
Functions
40.1
Function notation
40.2
Operations with functions
40.3
Adding functions
40.4
Subtracting functions
40.5
Multiplying functions
40.6
Dividing functions
40.7
Composite functions
40.8
Inequalities of combined functions
40.9
Inverse functions
40.10
One to one functions
40.11
Difference quotient: applications of functions