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Chapter 2: Q. 5 (page 69)

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

h(x)=3x-12

Short Answer

Expert verified

The domain of the given function is{x|x≥4}

Step by step solution

01

Step 1. Given Information 

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

h(x)=3x-12

02

Step 2. The function h tells us to take the square root of 3x-12.

But only non-negative numbers have real square roots, so the expression under the square root (the radicand) must be non-negative (greater than or equal to zero).

03

Step 3. This requires that

3x-12≥0

Add 12 on both side

3x-12+12≥0+123x≥12

Divide by 3 on both side

33x≥123

x≥4

04

Step 4. The domain of h is

{x|x≥4}

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Most popular questions from this chapter

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)=x2-1

If f(x)=-3xifx<-10ifx=-12x2+1ifx>-1

Find: (a)f(-2) and (b) f(-1) (c)f(0)

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 7–18, 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

Concepts and Vocabulary

A function f is ___________ on an open interval I if, for any choice of x1 and x2 in I, withx1<x2wehavef(x1)<f(x2)
See all solutions

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