# find the domain of the given 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 1.1, Problem 32E
To determine

## To find: find the domain of the given function.

Expert Solution

The domain of the function is, [2,3]

### Explanation of Solution

Given information:

The given function is,

g(t)=3t2+t

Concept used:

To represent the function:

A function f is a rule that assigns to each element x in a set D exactly one element called f(x) in a set E. The set D and E are sets of real numbers. The set D is called the domain of the function.

If f is a function with domain D .

Then the set of ordered pairs are.

{(x,f(x))|xD}

The given function is

g(t)=3t2+t

The square root a negative number is not defined (as a real number)

The domain of g consists of all value of t such that

3t0t3

And,

2+t0t2

Hence, the domain of g is

2t3

Therefore the domain of g is the interval,

[2,3]

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