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Chapter 5: Q. 88 (page 270)

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.

Short Answer

Expert verified

The function and inverse is

f(x)=x4,x≥0f-1(x)=x4,x≥0

Step by step solution

01

Given information

Given the functionf(x)=x4

02

Calculating the inverse

Calculating, we get

f(x)=x4y=x4x=y4y=x14f-1(x)=x14,x≥0

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Most popular questions from this chapter

the function f is one-to-one. Find its inverse and check your answer.

f(x)=x2-42x2x>0

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

f(x)=-3x+1x

Ideal Body Weight One model for the ideal body weight W for men (in kilograms) as a function of height h (in inches) is given by the function

W(h)=50+2.3h-60

(a) What is the ideal weight of a 6-foot male?

(b) Express the height has a function of weight W.

(c) Verify that h=Whis the inverse of W=Whby showing that role="math" localid="1646158219737" h(W(h))=h and W(h(W))=W.

(d) What is the height of a male who is at his ideal weight of 80 kilograms?

[Note: The ideal body weight W for women (in kilograms) as a function of height h (in inches) is given byrole="math" localid="1646159253780" Wh=45.5+2.3(h-60).

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

f(x)=-2xx-1

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

Solve:

x2+3x=4x
See all solutions

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