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- CLEP College Algebra
- Composite Functions and Inverses
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)