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3.4E: Composition of Functions (Exercises) - Mathematics


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 ight)^{-3}})


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