Find the domain of the function f ( x ) = 2 x 2 + 5 x + 3 2 x 2 − 5 x − 3

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Precalculus: Mathematics for Calcu...

6th Edition
Stewart + 5 others
Publisher: Cengage Learning
ISBN: 9780840068071

Solutions

Chapter 2, Problem 20RE
To determine

Find the domain of the function f(x)=2x2+5x+32x2−5x−3

Expert Solution

The domain of the function,

f(x)=2x2+5x+32x25x3 is [(,1.5)(1.5,1)(1,0.5)(0.5,3)(3,)]

Explanation of Solution

Given information: Consider the function f(x)=2x2+5x+32x25x3

Calculation:

For Numerator,

A rational expression is not defined when the denominator is 0.

Since ,

2x2+5x+302x2+2x+3x+302x(x+1)+3(x+1)0(2x+3)(x+1)0

Then,

x+10x1 and

Hence the Numerator in the given function is defined for all the values of x in the set of real numbers except of the values at x=1.5 and x=1 .

And for denominator,

A rational expression is not defined when the denominator is 0.

Since

2x+102x1x12x0.5 Then,

and

Hence the Denominator in the given function is defined for all the values of x in the set of real numbers except of the values at x=0.5 and x=3 .

Thus, the domain of the function,

f(x)=2x2+5x+32x25x3 is [(,1.5)(1.5,1)(1,0.5)(0.5,3)(3,)]

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