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Chapter 2: Q. 11 (page 124)

Find the domain of each function.

g(x)=xx+8

Short Answer

Expert verified

The domain of the functiong(x)=xx+8 is {x|x>-8}.

Step by step solution

01

Step 1. Given information 

We have been given a function g(x)=xx+8.

We have to find its domain.

02

Step 2. Find the values that make the function defined 

Square root function is defined for nonnegative numbers and also the numerator should not be zero.

Therefore x+8should be positive.

x+8>0x+8-8>0-8(Subtract8frombothsides)x>-8

Therefore, the domain will be {x|x>-8}.

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Most popular questions from this chapter

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.

g(x)=x2+3x2-1

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.

f(x)=-x

The domain of fgconsists of numbers xfor which g(x)____ 0that are in the domains of both ____ and ____.

If (1,3)is a point on the graph of y=f(x), which of the following points must be on the graph ofy=2f(x)?

In Problems 7–18, 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
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