# 3.4E: Composition of Functions (Exercises)

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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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