The domain and range of the function.

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Single Variable Calculus: Concepts...

4th Edition
James Stewart
Publisher: Cengage Learning
ISBN: 9781337687805

Solutions

Chapter 1, Problem 5RE
To determine

To find: The domain and range of the function.

Expert Solution

Solution:

The domain of the function f (x) is (,13)(13,).

The range of the function f (x) is (,0)(0,).

Explanation of Solution

Given:

The function f(x)=23x1.

Calculation:

The domain is the set of all input values of the function for which the function is real and defined.

Consider the denominator of the function f(x) and equate to zero and obtain the undefined point.

3x1=03x=1x=13

Hence, the function is undefined when x=13.

Therefore, the domain of the function is, {x|x13}.

And, the interval notation of the domain of f(x) is (,13)(13,).

The range is the set of all output values of the function.

Observe that the function f(x)=23x1 can have any values as output other than 0.

Thus, the range of the function is (,0)(0,).

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