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Chapter 2: Q. 9 (page 126)

For the functions f(x)=2x2+1and g(x)=3x-2, find

the following and simplify:

(a) f-g

(b) f路g

(c) f(x+h)-f(x)

Short Answer

Expert verified

For functions f(x)=2x2+1g(x)=3x-2

(a)(f-g)(x)=2x2-3x+3

(b) (f路g)(x)=6x3-4x2+3x-2

(c)f(x+h)-f(x)=4xh+2h2

Step by step solution

01

Step 1. given data

The given functions are

f(x)=2x2+1g(x)=3x-2

02

Step 2. Part (a)

The difference of functionf(x)&g(x)is

(f-g)(x)=f(x)-g(x)(f-g)(x)=2x2+1-(3x-2)(f-g)(x)=2x2-3x+3

03

Step 3. Part (b)

The product of functionsf(x)&g(x)is

(f路g)(x)=f(x)路g(x)(f路g)(x)=(2x2+1)(3x-2)(f路g)(x)=2x2(3x)-2x2(2)+(1)(3x)-(1)(2)(f路g)(x)=6x3-4x2+3x-2

04

Step 4. Part (c)

Substitute x+h for x in the function f(x)

f(x)=2x2+1f(x+h)=2(x+h)2+1 f(x+h)=2(x2+2xh+h2)+1f(x+h)=2x2+4xh+2h2+1

sorole="math" localid="1645903721224" f(x+h)-f(x)=(2x2+4xh+2h2+1)-(2x2+1)f(x+h)-f(x)=2x2+4xh+2h2+1-2x2-1f(x+h)-f(x)=4xh+2h2

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