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Chapter 2: Q. 7 (page 124)

Find the domain of each function.

f(x)=2-x

Short Answer

Expert verified

The domain of the function is {x|x≤2}.

Step by step solution

01

Step 1. Given information 

We have been given a function f(x)=2-x.

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.

Therefore, (2-x)should be non-negative.

2-x≥02-x+x≥0+x(Addxonbothsides)2≥xx≤2

Therefore, the domain is {x|x≤2}.

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Most popular questions from this chapter

The short-term

(no more than 24hours) parking fee F (in dollars) for

parking x hours at O’Hare International Airport’s main

parking garage can be modeled by the function

role="math" localid="1645828501222" F(x)=2if0<x≤14if1<x≤310if3<x≤45int(x+1)+2if4<x<951if9≤x≤24

Determine the fee for parking in the short-term parking

garage for

(a) 2hours

(b) 7hours

(c) 15hours

(d) 8hours and 24minutes

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+23-3

True or False The domain of (f.g)(x)consists of the numbers x that are in the domains of both fandg.

Graph y=x. Then on the same screen graph y=2x, followed by y=4x, followed by

y=12x.What pattern do you observe? Can you predict the graph ofy=14x? ofy=5x

?

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
See all solutions

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