Question

Find f(g(x)) and g(f(x)) and determine whether the pair of functions f and g are inverses of each other.f(x) = 8x-2 and g(x) = x+8/2a. f(g(x)) =

Answer 1

The fuction f(g(x)) is given by

$\begin{gathered} \text{f(g(x))}=f(\frac{x+8}{2}) \\ =8(\frac{x+8}{2})-2 \\ =4(x+8)-2 \\ =4x+32-2 \\ =4x+30 \end{gathered}$

The function g(f(x)) is

$\begin{gathered} g(f(x))=g(8x-2) \\ =\frac{(8x-2)-2}{2} \\ =\frac{8x-4}{2} \\ =4x-2 \end{gathered}$

The functions f and g will be inverses of each other if the function values obtained is x in both cases. But, we got 4x+30 for f(g(x) and 4x-2 for g(f(x)), which are not equal to x. So, f and g are not inverses of each other.