Question

for function f use composition of functions to show the f^-1 is as given. you may use composition of functions or find a formula for the inverse. let f(x) = x-9/3 show that f^-1(x)=3x+9

Answer 1

If f^(-1)(x) is the inverse of f(x), then f( f^-1(x) ) = x.
Find f( f^-1(x) ) and if it is x, then f^(-1)(x) is the inverse of f(x).

Answer 2

\[
f(x) = \frac{x-9}{3} \\
f(f^{-1}(x)) = \frac{3x+9-9}{3} = \frac{3x}{3} = x\\
\]Therefore, 3x+9 is the inverse of f(x).