Answer to Question #237901 in Calculus for CCW

Question

Unit 1 Review:

2) Find f(g(x)) and g(f(x)) given f(x) = 2x+8 and g(x) = 1/2x - 4

Answer 1

Let $f(x) = 2x+8$ and $g(x) = \frac{1}{2x - 4}.$

Then $f(g(x))=f(\frac{1}{2x - 4}) =2\cdot\frac{1}{2x - 4}+8=\frac{2+16x-32}{2x-4}=\frac{16x-30}{2x-4}=\frac{8x-15}{x-2},$

$g(f(x)) =g(2x+8)=\frac{1}{2(2x+8) - 4}=\frac{1}{4x+12}.$