Q. 86 - Precalculus Enhanced with Graphing Utilities

Question

A function $f$ has an inverse function. If the graph of $f$ lies in quadrant II, in which quadrant does the graph of  $f^{-1}$lie?

Step-by-Step Solution

Answer

The graph of $f^{-1}$ lies in the $4th$ quadrant

Step 1: Given information

Given the function $f$ has an inverse function

Step 2: Checking the reason

The graphs of a function $f$and its inverse are mirror images (or reflections) of each other about the line $y=x$.

Hence, if the graph of a function $f$ is in Quadrant II, then the graph of its inverse is its reflection about the line $y=x$. Note that when a graph in Quadrant II is reflected about the line $y=x$, the reflection is also in Quadrant IV.