Q. 75 - Precalculus Enhanced with Graphing Utilities

Question

If $f\left(7\right)=3$ and f is one-to-one, what is$f^{-1}\left(13\right)$?

Step-by-Step Solution

Answer

If the function $f$ is one to one function and$f\left(7\right)=3$ then $f^{-1}\left(13\right)=7$

Step 1. Given data

Function f is one to one function

$f\left(7\right)=13$

Step 2. inverse function value

If a function $f\left(x\right)$ is one to one function

and $f\left(a\right)=b$

then$f^{-1}\left(b\right)=a$

as $f\left(7\right)=13$

so $f^{-1}\left(13\right)=7$