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Chapter 5: Q 58. (page 269)

The function fx=-3xis 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=-3xis f-1x=-3x. Graph is shown below.

Step by step solution

01

Step 1. Given information.

Given a one-to-one functionfx=-3x.

02

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

To find the explicit form of the inverse solve x=-3y for y.

It can be seen that y=-3x.

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

Prove ff-1x=xas follows.

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

Prove f-1fx=xas follows.

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

Therefore,f-1x=-3xis inverse offx=-3x.

03

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

Graph fx=-3x,f-1x=-3xand y=xas follows.

Note that function f and its inverse is one and the same. So, the graph for both coincides.

Broken blue color line represents the function f and unbroken orange color line represents its inverse.

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