Q 7. - Precalculus Enhanced with Graphing Utilities

Question

If f is a one-to-one function and $f\left(3\right)=8$, then $f^{-1}\left(8\right)=$$\dots \dots$

Step-by-Step Solution

Answer

if $f$ is a one-to-one function and $f\left(3\right)=8$, then$f^{-1}\left(8\right)=3$

Step 1. Definition of inverse function

An inverse function is a function that returns the original value for which a function has given the output. If $f\left(x\right)$ is a function which gives output $y$, then the inverse function of $y$, i.e.$f^{-1}\left(y\right)$ will return the value $x$.

Step 2. Explanation

Given that $f$ is one-to-one function and $f\left(3\right)=8$.

Then according to definition of inverse function$f^{-1}\left(8\right)=3$.