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Chapter 2: Q. 49 (page 69)

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

f(x)=xx2+1

Short Answer

Expert verified

The domain of the given function is the set of all real numbers.

Step by step solution

01

Step 1. Given Information

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

f(x)=xx2+1

02

Step 2. The function tells us to divide x by x2+1.

Since these operations can be performed on any real number, we conclude that the domain of f is the set of all real numbers.

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Most popular questions from this chapter

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

If (3,6)is a point on the graph of y=f(x), which of the following points must be on the graph ofy=f(-x)?

Exploration Graph y=x2,y=x4, and y=x6 on the same screen. What do you notice is the same about each graph? What do you notice that is different?

A right triangle has one vertex on the graph of y=9-x2,x>0, at x,y, another at the origin, and the third on the positive x-axis at x,0. Express the area Aof the triangle as a function of 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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