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 30E
To determine

To find: find the domain of the given function.

Expert Solution

Answer to Problem 30E

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

Explanation of Solution

Given information:

The given function is,

  f(x)=2x35x2+x6

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(x)=2x35x2+x6

The factors of denominator of the function is calculated as,

  x2+x6=0x2+3x2x6=0(x+3)(x2)=0

The division by 0 is not allowed so The function f(x) is not defined when the denominator (x+3)(x2)0

The domain of f consists of all value of x

  x+3=0x=3,x2=0x=2

Thus, the domain of f is

  {x|x2,x3}

Therefore the domain of f is the interval,

  [2,3]

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