Answer
a) Finding the inverse
$f^{-1}(x) = x -5$
b) Verifying that it is the correct inverse
$f(f^{-1}(x)) = x$
$f(x-5) = (x - 5) + 5$
$= x - 5 + 5$
$= x$
$f^{-1}(f(x)) = x$
$f^{-1}(x+5) = (x+5) - 5$
$= x + 5 - 5$
$= x$
Therefore, the inverse equation is correct.
Work Step by Step
a) Finding the inverse
Let $f(x) = y$
$y = x + 5$
$x = y + 5$
$x - 5 = y$
$y = x - 5$
$f^{-1}(x) = x -5$
b) Verifying that it is the correct inverse
$f(f^{-1}(x)) = x$
$f(x-5) = (x - 5) + 5$
$= x - 5 + 5$
$= x$
$f^{-1}(f(x)) = x$
$f^{-1}(x+5) = (x+5) - 5$
$= x + 5 - 5$
$= x$
Therefore, the inverse equation is correct.
