# 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 31E
To determine

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

Expert Solution

The domain of the function is [,] ,

### Explanation of Solution

Given information:

The given function is,

f(t)=2t13

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

f(t)=2t13

We take f(t)=r to get the values of t of the function so calculated as,

2t13=r2t1=r32t=r3+1t=r3+12

The cube root an odd number is not defined (as a real number)

The domain of f consists of all value of t

r3>0,r3<0,r3=0

Now,

r3,r3

Then,

t±

Thus, the domain of f is

{tR|t,t}

Hence, this function is defined for all real number.

Therefore the domain of f(t) is the interval,

[,]

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