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Chapter 3: Q. 315 (page 327)

In the following exercises, evaluate the function:

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

Function:g(x)=2x+1

Short Answer

Expert verified

a.g(h2)=2h2+1b.g(x+2)=2x+5c.g(x)+g(2)=2x+6

Step by step solution

01

Step 1. Given Information

The given function isg(x)=2x+1.

02

Part (a) Step 1.  Evaluating g(h2)

To evaluate g(h2)substitute h2for x.

g(h2)=2(h2)+1g(h2)=2h2+1g(h2)=2(h2)+1g(h2)=2h2+1

Therefore, g(h2)=2h2+1.

03

Part (b) Step 1.  Evaluating g(x+2).

To evaluate g(x+2)substitute x+2for x.

g(x+2)=2(x+2)+1g(x+2)=2x+4+1g(x+2)=2x+5

Therefore,g(x+2)=2x+5.

04

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

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

g(2)=2(2)+1g(2)=5

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

g(x)+g(2)=2x+1+5g(x)+g(2)=2x+6

Therefore,g(x)+g(2)=2x+6.

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