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Chapter 2: Q. 44 (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)=x2+x

Short Answer

Expert verified

The value of

f(0)=0f(1)=2f(-1)=0f(-x)=x2-x-f(x)=-x2+xf(x+1)=x2+3x+2f(x)=x2+xf(x+h)=x2+h2+2xh+x+h

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)=x2+x

02

Part (a) Step 1. We find the value of  f(0)Putting x=0 in the given question.

f(0)=02+0f(0)=0

03

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

f(1)=(1)2+1f(1)=1+1f(1)=2

04

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

f(-1)=(-1)2+(-1)f(-1)=1-1f(-1)=0

05

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

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

06

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

-f(x)=-x2+x

07

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

f(x+1)=(x+1)2+x+1

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

localid="1645962442431" f(x+1)=x2+2x+1+x+1f(x+1)=x2+3x+2

08

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

The value off(x)=x2+x

09

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

f(x+h)=(x+h)2+x+h

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

f(x+h)=x2+2xh+h2+x+hf(x+h)=x2+h2+2xh+x+h

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