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Chapter 2: Q. 62 (page 69)

In Problems 47鈥� 62, find the domain of each function.

h(z)=z+3z-2

Short Answer

Expert verified

The domain of the given function is{z|z鈮�-3,z鈮�2}

Step by step solution

01

Step 1. Given Information 

In the given problems we have to find the domain of given function.

h(z)=z+3z-2

02

Step 2. The function h tells us to take the square root of z+3 and divide this result by z-2.

This requires that

z+3鈮�0

Subtract 3 on both side and change the inequality

z+3-3鈮�0-3z鈮�-3

Andz-2鈮�0

Add 2 on both side

z-2+2鈮�0+2z鈮�2

03

Step 3. Combining these two restrictions,

The domain of h is

{z|z鈮�-3,z鈮�2}

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Most popular questions from this chapter

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

The interval (2, 5) can be written as the inequality ___________

In Problems 33鈥� 44, determine algebraically whether each function is even, odd, or neither.
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Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.g(x)=x3-1

True or False

To obtain the graph of f(x)=x3+5,shift the graph of y=x3vertically up 5units.
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