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Chapter 2: Q. 10 (page 124)

Find the domain of each function.

f(x)=x+1x2-4

Short Answer

Expert verified

The domain of the functionf(x)=x+1x2-4 is role="math" localid="1645963482579" {x|x鈮�-1;x鈮�2}.

Step by step solution

01

Step 1. Given information 

We have been given a function f(x)=x+1x2-4.

We have to find its domain.

02

Step 2. Find the values that make the square root function undefined

Square root function is defined for nonnegative numbers.

Therefore, (x+1)should be non-negative.

x+1鈮�0x+1-1鈮�0-1(Subtract1frombothsides)x鈮�-1

03

Step 3. Find the values where the denominator becomes zero 

The given function will not be defined where the denominator becomes zero.

We need to exclude those values of x.

x2-4=0x2-4+4=0+4(Add4onbothsides)x2=4x=卤4(Takesquarerootsonbothsides)x=卤2

Therefore, the domain will be {x|x鈮�-1;x鈮�2}.

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Most popular questions from this chapter

Exploration Graph y=x. Then on the same screen graph y=-x. What pattern do you observe? Now try y=2x+1 and y=2(-x)+1. What do you conclude?

Match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function

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

A semicircle of radius r is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure.

(a) Express the area A of the rectangle as a function of the radius r of the semicircle.

(b) Express the perimeter p of the rectangle as a function of r.

Suppose that the graph of a function gis known. The graph of y=g(x)+2may be obtained by a _______ shift of the graph of g ________ a distance of 2 units.
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