Question

F(x)=-3/4x+9 what are the steps for finding f^-1(x)

Answer 1

The inverse function $f^{-1}(x)$ is such that

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

If $f(x)=-\frac34x+9$, then we have

$f\left(f^{-1}(x)\right) = -\dfrac34f^{-1}(x)+9 = x$

Solve for the inverse :

$-\dfrac34f^{-1}(x)+9 = x \\\\ -\dfrac34f^{-1}(x) = x-9 \\\\ f^{-1}(x) = -\dfrac43(x-9) \\\\ \boxed{f^{-1}(x) = -\dfrac43x+12}$