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Q. 85

Expert-verifiedFound in: Page 270

Book edition
6th

Author(s)
Sullivan

Pages
1200 pages

ISBN
9780321795465

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

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

Given the function $f$ has an inverse function

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 I, then the graph of its inverse is its reflection about the line $y=x$. Note that when a graph in Quadrant I is reflected about the line $y=x$, the reflection is also in Quadrant I.

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