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Chapter 3: Q. 319 (page 327)

In the following exercises, evaluate the function:

a.g(h2)b.g(x+2)c.g(x)+g(2)

Function: g(x)=3-x

Short Answer

Expert verified

For the function g(x)=3-x,we have,

a.g(h2)=3-h2b.g(x+2)=1-xc.g(x)+g(2)=4-x

Step by step solution

01

Step 1. Given Information

The given function isg(x)=3-x.

02

Part (a) Step 1. Evaluating g(h2)

To evaluate g(h2),substitute h2for role="math" x.

role="math" g(h2)=3-(h2)g(h2)=3-h2

Therefore,g(h2)=3-h2

03

Part (b) Step 1. Evaluating g(x+2).

To evaluate g(x+2),substitute x+2for role="math" x.

role="math" g(x+2)=3-(x+2)g(x+2)=3-x-2g(x+2)=1-x

Therefore,g(x+2)=1-x.

04

Part(c) Step 1. Evaluating g(x)+g(2)

To evaluate g(x)+g(2)first find role="math" g(2)

g(2)=3-2g(2)=1

Now find role="math" g(x)+g(2)

role="math" g(x)+g(2)=3-x+1g(x)+g(2)=4-x

Therefore,g(x)+g(2)=4-x.

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