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?

Short answer

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

Step-by-step solution

Given information

Given the function$f$has an inverse function

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.