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Chapter 5: Q. 66 (page 269)

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

f(x)=-3x+1x

Short Answer

Expert verified

The inverse off is-1x+3.

Step by step solution

01

Step 1. Given Information 

The given function isfx=-3x+1x

We have to find its inverse and check the answer.

02

Step 2. Replace f(x) with y and interchange the variables x and y 

So,y=-3x+1x

Interchange the variables

x=-3y+1y.

03

Step 3. Solve for y 

x=-3y+1yxy=-3y-1xy+3y=-1yx+3=-1y=-1x+3

The inverse isf-1x=-1x+3

04

Step 4. Check the answer 

We can check the answers by f-1fxandff-1x.

So,

f-1fx=f-1-3x+1x=-1-3x+1x+3=-x-1=x

Thus, f-1fx=x

Now,

ff-1x=f-1x+3=-3-1x+3+1-1x+3=-x-1=x

Thus, ff-1x=x

Hence our result is right.

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Most popular questions from this chapter

solve each equation. Verify your results using a graphing utility.

ex=e3x+8

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.

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.

Use transformations to graph the function. Determine the domain, range and horizontal asymptote of the function.

fx=1-2-x/3
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