BuyFind

Single Variable Calculus: Concepts...

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

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

Answer to Problem 31E

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,

  [,]

Have a homework question?

Subscribe to bartleby learn! Ask subject matter experts 30 homework questions each month. Plus, you’ll have access to millions of step-by-step textbook answers!