Answer
a) Finding the inverse
$f^{-1}(x) = x - 3$
$f(f^{-1}(x)) = x$
$f(x-3) = (x - 3) + 3$
$= x - 3 + 3$
$= x$
b) Verification
$f^{-1}(f(x)) = x$
$f^{-1}(x+3) = (x+3) - 3$
$= x + 3 - 3$
$= x$
Therefore, the inverse equation is correct.
Work Step by Step
a) Find the inverse function of $f(x)$. Let $f(x) = y$
$y = x+ 3$
$x = y + 3$
$x - 3 = y$
$y = x- 3$
$f^{-1}(x) = x - 3$
b) Verifying that the equation is correct
$f(f^{-1}(x)) = x$
$f(x-3) = (x - 3) + 3$
$= x - 3 + 3$
$= x$
$f^{-1}(f(x)) = x$
$f^{-1}(x+3) = (x+3) - 3$
$= x + 3 - 3$
$= x$
Therefore, the inverse equation is correct.
