Question

f(x) = x + 7
Work out an expression for f-1(x).

Answer 1

If $f^{-1}(x)$ is the inverse of $f(x)$, then

$f\left(f^{-1}(x)\right) = x$

Given $f(x)=x+7$, the inverse is such that

$f\left(f^{-1}(x)\right) = f^{-1}(x)+7 = x$

Solve for $f^{-1}(x)$ :

$f^{-1}(x)+7=x \implies \boxed{f^{-1}(x)=x-7}$