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Chapter 3: Q. 317 (page 327)

In the following exercises, evaluate the function:

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

Function: g(x)=-3x-2

Short Answer

Expert verified

For the function, g(x)=-3x-2,we have,

a.g(h2)=-3h2-2b.g(x+2)=-3x-8c.g(x)+g(2)=-3x-10

Step by step solution

01

Step 1. Given Information

The given function isg(x)=-3x-2.

02

Part (a) Step 1. Evaluating g(h2)

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

g(h2)=-3(h2)-2g(h2)=-3h2-2

Therefore,g(h2)=-3h2-2

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)-2g(x+2)=-3x-6-2g(x+2)=-3x-8

Therefore,g(x+2)=-3x-8.

04

Part (c) Step 1. Evaluating g(x)+g(2)

To evaluate g(x)+g(2),first find the value of role="math" g(2).

To findg(2),substitute2forx.

role="math" g(2)=-3(2)-2g(2)=-6-2g(2)=-8

Now find g(x)+g(2).

g(x)+g(2)=-3x-2+(-8)g(x)+g(2)=-3x-2-8g(x)+g(2)=-3x-10

Therefore,g(x)+g(2)=-3x-10.

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