5.1E: Composition of Functions (Exercises)

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Nov 16, 2021
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- 5.1: Algebra of Functions and Compositions
- 5.2: Inverse Functions

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For the following exercises, find $(f \circ g)(x)$ and $(g \circ f)(x)$ for each pair of functions.

34. $f(x)=4-x, \quad g(x)=-4 x$
35. $f(x)=3 x+2, \quad g(x)=5-6 x$
36. $f(x)=x^{2}+2 x, \quad g(x)=5 x+1$
37. $f(x)=\sqrt{x+2}, \quad g(x)=\frac{1}{x}$
38. $f(x)=\frac{x+3}{2}, \quad g(x)=\sqrt{1-x}$

For the following exercises, find $(f \circ g)$ and the domain for $(f \circ g)(x)$ for each pair of functions.

39. $f(x)=\frac{x+1}{x+4}, \quad g(x)=\frac{1}{x}$
40. $f(x)=\frac{1}{x+3}, \quad g(x)=\frac{1}{x-9}$
41. $f(x)=\frac{1}{x}, \quad g(x)=\sqrt{x}$
42. $f(x)=\frac{1}{x^{2}-1}, \quad g(x)=\sqrt{x+1}$

For the following exercises, express each function $H$ as a composition of two functions $f$ and $g$ where $H(x)=(f \circ g)(x)$ .

43. $H(x)=\sqrt{\frac{2 x-1}{3 x+4}}$
44. $H(x)=\frac{1}{\left(3 x^{2}-4\right)^{-3}}$

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