For the following exercises, find (f∘g)(x) and (g∘f)(x) for each pair of functions.
34. f(x)=4−x,g(x)=−4x
35. f(x)=3x+2,g(x)=5−6x
36. f(x)=x2+2x,g(x)=5x+1
37. f(x)=√x+2,g(x)=1x
38. f(x)=x+32,g(x)=√1−x
For the following exercises, find (f∘g) and the domain for (f∘g)(x) for each pair of functions.
39. f(x)=x+1x+4,g(x)=1x
40. f(x)=1x+3,g(x)=1x−9
41. f(x)=1x,g(x)=√x
42. f(x)=1x2−1,g(x)=√x+1
For the following exercises, express each function H as a composition of two functions f and g where H(x)=(f∘g)(x).
43. H(x)=√2x−13x+4
44. H(x)=1(3x2−4)−3