Answer
a.
$f^{-1}(x) = 4x-4$
b.
$f(f^{-1}(x)) = (4x-4)/4 + 1$
$f(f^{-1}(x)) = x - 1 + 1$
$f(f^{-1}(x)) = x$
$f^{-1}(f(x)) = 4(x/4 - 1) + 4$
$f^{-1}(f(x)) = x - 4 + 4$
$f^{-1}(f(x)) = x $
Work Step by Step
a.
To find the inverse of a function $f(x)$, switch $f(x)$ with $x$ and replace $f(x)$ with $f^{-1}(x)$
$f(x) = x/4 + 1$
$x = f^{-1}(x)/4 + 1$
$x - 1 = f^{-1}(x)/4$
$4x-4 = f^{-1}(x)$
$f^{-1}(x) = 4x-4$
b.
$f(f^{-1}(x)) = (4x-4)/4 + 1$
$f(f^{-1}(x)) = x - 1 + 1$
$f(f^{-1}(x)) = x$
$f^{-1}(f(x)) = 4(x/4 - 1) + 4$
$f^{-1}(f(x)) = x - 4 + 4$
$f^{-1}(f(x)) = x $
