Question

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

Short answer

As the graph of the function $y=f\left(x\right)$decreases on the interval$(0,5)$, the graph of its inverse function role="math" localid="1646177037888" $y=f^{-1}\left(x\right)$will be decreasing on the intervalrole="math" localid="1646177008240" $(0,5)$

Step-by-step solution

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 xand 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 $(0,5)$