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Chapter 5: Q. 64 (page 269)

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

f(x)=-2xx-1

Short Answer

Expert verified

The inverse off isxx+2.

Step by step solution

01

Step 1. Given Information 

The given function isfx=-2xx-1

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=-2xx-1

Interchange the variables

x=-2yy-1

03

Step 3. Solve for y 

x=-2yy-1xy-1=-2yxy-x=-2yxy+2y=xyx+2=xy=xx+2

The inverse isf-1(x)=xx+2.

04

Step 4. Check the answer 

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

So,

f-1fx=f-1-2xx-1=-2xx-1-2xx-1+2=-2x-2=x

Thus, f-1fx=x

Now,

ff-1x=fxx+2=-2xx+2xx+2-1=-2x-2=x

Thus, ff-1x=x

Hence our result is right.

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