To evaluate f ( x ) = 2 x 2 + 3 x − 4 at a number, we substitute the number for x in the definition of f ( x ) .

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 2.1, Problem 23E
To determine

To evaluate f(x)=2x2+3x−4 at a number, we substitute the number for x in the definition of f(x) .

Expert Solution

The value of the given functionare:

f(0)=4,f(2)=10,f(2)=2,f(2)=32,f(x+1)=2x2+7x+1,f(x)=2x23x4

Explanation of Solution

Given information: consider the function f(x)=2x2+3x4

Calculation:

Evaluate the values of the function f(x)=2x2+3x4 for the given values of the variable x

Plug the value x=0, in the function f(x)=2x2+3x4 then we get the value of f(0).

f(0)=2(0)2+3(0)4f(0)=0+04f(0)=4

Plug the value x=2, in the function f(x)=2x2+3x4 then we get the value of f(2).

f(2)=2(2)2+3(2)4f(2)=2(4)+3(2)4f(2)=8+64f(2)=10

Plug the value x=2, in the function f(x)=2x2+3x4 then we get the value of f(2).

f(2)=2(2)2+3(2)4f(2)=2(4)+3(2)4f(2)=864f(2)=2

Plug the value x=2, in the function f(x)=2x2+3x4 then we get the value of f(2).

f(2)=2(2)2+3(2)4f(2)=2(2)+3(2)4f(2)=4+3(2)4f(2)=3(2)

Plug the value x=x+1, in the function f(x)=2x2+3x4 then we get the value of f(x+1).

f(x+1)=2(x+1)2+3(x+1)4f(x+1)=2(x2+2x+1)+3(x+1)4f(x+1)=2x2+4x+2+3x+34f(x+1)=2x2+7x+54f(x+1)=2x2+7x+1

Plug the value x=x, in the function f(x)=2x2+3x4 then we get the value of f(x).

f(x)=2(x)2+3(x)4f(x)=2x23x4

Thus, the values of the given functionare:

f(0)=4,f(2)=10,f(2)=2,f(2)=32,f(x+1)=2x2+7x+1,f(x)=2x23x4

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