Inverse function

Text

Given $f(x)=3x-6$, find the inverse function and compute $f^{-1}(9)$.

Solution

The function is linear, hence injective. Set $y=3x-6$ and solve for $x$: $x=\frac{y+6}{3}\;\Rightarrow\; f^{-1}(x)=\frac{x+6}{3}.$ So $f^{-1}(9)=\dfrac{9+6}{3}=5$. $\boxed{\,f^{-1}(x)=\dfrac{x+6}{3},\quad f^{-1}(9)=5\,}$