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Chapter 5: Q 10. (page 267)

True or False If fand gare inverse functions, the domain of f is the same as the range of g.

Short Answer

Expert verified

Its true, If fand gare inverse functions, the domain of fis the same as the range ofg.

Step by step solution

01

Step 1. Given

Given thatfandgare inverse function.

02

Step 2. Explanation

If fxand f-1xare inverse functions, then domain of fxis same as the range of f-1x.

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Most popular questions from this chapter

The domain of a one-to-one functionf is[5,鈭�) , and its range is[-2,鈭�). State the domain and the range off-1 .

The function f(x)=x4is 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.

The domain of one-to-one function g is0,15, and range is (0,8). State the domain and range oflocalid="1646180141229" g-1

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

f(x)=3x+42x-3

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

True or False

The function f(x)=2xx-3 hasy=2 as a horizontal asymptote.
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