Chapter 5: Q. 86 (page 270)

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

Expert verified

The graph of $f^{- 1}$ lies in the $4 t h$ 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.

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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

Step by step solution

Given information

Checking the reason

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A function fhas an inverse function. If the graph of f lies in quadrant II, in which quadrant does the graph of f-1lie?

Short Answer

Step by step solution

Given information

Checking the reason

One App. One Place for Learning.

Most popular questions from this chapter

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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?