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Chapter 5: Q. 85 (page 270)

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

Short Answer

Expert verified

The graph off-1lies in the first quadrant

Step by step solution

01

Given information

Given the functionfhas an inverse function

02

Checking the reason

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

Hence, if the graph of a function fis 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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Most popular questions from this chapter

The function f(x)=|x|is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of f.

Begin with the graph of y=exand use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=9-3e-x

In Problems 61鈥�72, the function f is one-to-one. Find its inverse and check your answer.

f(x)=-2xx-1

If f(x)=ax+band g(x)=cx+d, then find: -

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Begin with the graph of y=exand use transformation to graph the function. Determine the domain, range and horizontal asymptote of the function.

localid="1646160286433" fx=5-e-x
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