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Chapter 2: Q. 39 (page 69)

In Problems 39鈥� 46, find the following for each function:

(a)f(0)(b)f(1)(c)f(-1)(d)f(-x)(e)-f(x)(f)f(x+1)(g)f(x)(h)f(x+h)

f(x)=3x2+2x-4

Short Answer

Expert verified

The value of

f(0)=-4f(1)=1f(-1)=-3f(-x)=3x2-2x-4-f(x)=-3x2-2x+4f(x+1)=3x2+8x+1f(x)=3x2+2x-4f(x+h)=3x2+6xh+3h2+2x+2h-4

Step by step solution

01

Step 1. Given Information

We have to find the value for each function:

(a)f(0)(b)f(1)(c)f(-1)(d)f(-x)(e)-f(x)(f)f(x+1)(g)f(x)(h)f(x+h)

The given equation isf(x)=3x2+2x-4.

02

Part (a) Step 1. The given function is f(x)=3x2+2x-4

We find the value off(0)

03

Part (a) Step 2. Putting x=0 i the given equation.

f(0)=3(0)2+2脳0-4f(0)=0+0-4f(0)=-4

04

Part (b) Step 1. We find the value of f(1)Putting x=1 in the given question.

f(1)=3(1)2+2(1)-4f(1)=3脳1+2-4f(1)=3+2-4f(1)=1

05

Part (c) Step 1. We find the value of f(-1)Putting x=-1 in the given question.

f(-1)=3(-1)2+2(-1)-4f(-1)=3脳1-2-4f(-1)=3-2-4f(-1)=-3

06

Part (d) Step 1. We find the value of f(-x)Putting x=-x in the given question.

f(-x)=3(-x)2+2(-x)-4f(-x)=3x2-2x-4

07

Part (e) Step 1. We find the value of -f(x)To find the value we multiply the given equation by -1

-f(x)=-(3x2+2x-4)-f(x)=-3x2-2x+4

08

Part (f) Step 1. We find the value of f(x+1)Putting x=x+1 in the given question.

f(x+1)=3(x+1)2+2(x+1)-4

Using the formula (a+b)2=a2+2ab+b2

f(x+1)=3(x2+2x+1)+2x+2-4f(x+1)=3x2+6x+3+2x+2-4

Simplify

f(x+1)=3x2+8x+1

09

Part (g) Step 1. We find the value of f(x)

The value off(x)=3x2+2x-4

10

Part (h) Step 1. We find the value of f(x+h)Putting x=x+h in the given question.

f(x+h)=3(x+h)2+2(x+h)-4

Using the formula (a+b)2=a2+2ab+b2

f(x+h)=3(x2+2xh+h2)+2x+2h-4f(x+h)=3x2+6xh+3h2+2x+2h-4

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Most popular questions from this chapter

In Problems 7鈥�18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

True or False The domain of (f.g)(x)consists of the numbers x that are in the domains of both fandg.

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Part (a): Express the circumference Cof the circle as a function of x.

Part (b): Express the areaAof the circle as a function ofx.

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