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Chapter 5: Q 50. (page 269)

The function fx=-4xis one-to-one. Find its inverse and check the answer. Graph f,f-1 and y=x on the same coordinate axes.

Short Answer

Expert verified

Inverse of the function fx=-4xis f-1x=-x4. Graph is shown below.

Step by step solution

01

Step 1. Given information.

Given a one-to-one functionfx=-4x.

02

Step 2. Find the inverse of the function f and verify.

To find the explicit form of the inverse solve x=-4y for y.

It can be seen that y=-x4.

Note that if fgx=xand gfx=x, then fand g are inverse of one another.

Prove ff-1x=xas follows.

ff-1x=f-x4=-4-x4=x

Prove f-1fx=xas follows.

f-1fx=f-1-4x=--4x4=x

Therefore, f-1x=-x4is inverse of the functionfx=-4x.

03

Step 3. Graph f,f-1 and y=x on the same coordinate axes.

Graph fx=-4x,f-1x=-x4and y=xas follows.

Note the symmetry of the graphs with respect to the line y=x.

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