Q. 82 - Precalculus Enhanced with Graphing Utilities

Question

A function $y=f\left(x\right)$is decreasing on the interval$(0,5).$ What conclusions can you draw about the graph of $y=f^{-1}\left(x\right)$?

Step-by-Step Solution

Answer

As the graph of the function $y=f\left(x\right)$decreases on the interval$(0,5)$, the graph of its inverse function $y=f^{-1}\left(x\right)$ will be decreasing on the interval $(0,5)$

Step 1. Given data

Graph of function $y=f\left(x\right)$ increases on interval$(0,5)$

Step 2. description

Graph of Function $y=f\left(x\right)$ increasing

so y values of the function $y=f\left(x\right)$decrease as x values increases

the inverse function  is the interchange of x and y values of the function $y=f\left(x\right)$

so y values of inverse function  $y=f^{-1}\left(x\right)$will increase as x value decreases 

Thus inverse function$y=f^{-1}\left(x\right)$ will also decrease on interval $(0,5)$