Finding the Inverse of a Function

Problem 256: If $f(x) = x + 5$ , find the inverse function $f^{-1}(x)$ .

Solution: We will let $y = f(x)$ so that

$f(x) = x + 5 \implies y = x + 5.$

Now, we switch $x$ and $y$ .

$y = x + 5 \implies x = y + 5$

Solve for $y$ .

$x = y + 5 \implies y = x - 5$

The new found $y$ we call it $f^{-1}(x)$ . Thus,

$f^{-1}(x) = x - 5.$