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Chapter 3: Q. 318 (page 327)

In the following exercises, evaluate the function:

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

Function:g(x)=-8x+2

Short Answer

Expert verified

For the function, g(x)=-8x+2,we have,

a.g(h2)=-8h2+2b.g(x+2)=-8x-14c.g(x)+g(2)=-8x-12

Step by step solution

01

. Given Information

The given function isg(x)=-8x+2

02

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

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

g(h2)=-8(h2)+2g(h2)=-8h2+2

Therefore,g(h2)=-8h2+2

03

Part (b) Step 1. Evaluating g(x+2).

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

g(x+2)=-8(x+2)+2g(x+2)=-8x-16+2g(x+2)=-8x-14

Therefore,g(x+2)=-8x-14.

04

Part (c) Step 1. Evaluating g(x)+g(2).

To evaluate g(x)+g(2),first find g(2).

To find g(2),substitute 2for x.

g(2)=-8(2)+2g(2)=-16+2g(2)=-14

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

g(x)+g(2)=-8x+2+(-14)g(x)+g(2)=-8x+2-14g(x)+g(2)=-8x-12

Therefore,g(x)+g(2)=-8x-12.

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