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Chapter 2: Q. 13 (page 68)

True or False If no domain is specified for a function f, then the domain of fis taken to be the set of real numbers.

Short Answer

Expert verified

The given statement is true.

Step by step solution

01

Step 1. Given information 

In the given question we have to explain the given statement is true or false.

The statement is "If no domain is specified for a function f, then the domain of fis taken to be the set of real numbers. "

02

The domain of a function 

The domain of a function f(x) is the set of all values for which the function is defined, and the range of the function is the set of all values that f takes

03

Step 3. If a function f is defined by an equation and no domain is specified, then the domain will be taken to be the largest set of real numbers for which the equation defines a real number.

Hence, the given statement is true.

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Most popular questions from this chapter

In March 2011, Nicor Gas had the following rate schedule for natural gas usage in single-family residences:

Monthly customer charge -\(13.55

Distribution charge

First 20therms-0.1473/therm

Next 30therm -\)0.0579/therm

Over 50therm -\(0.0519/therm

Gas supply charge-\)0.51/therm

(a) What is the charge for using 40therms in a month?

(b) What is the charge for using 150therms in a month?

(c) Develop a model that gives the monthly charge Cfor x therms of gas.

(d) Graph the function found in part (c).

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.

g(x)=-x3

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)

A circle of radius ris in inscribed in a square. See the figure.

Part (a): Express the area A of the square as a function of the radius rof the circle.

Part (b): Express the perimeter p of the square as a function of the radius rof the circle.

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.

g(x)=4x
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