# f + g if f ( x ) = x 2 − 3 x + 2 and g ( x ) = 4 − 3 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, Problem 75RE

(a)

To determine

## To find: f+g if f(x)=x2−3x+2 and g(x)=4−3x

Expert Solution

f+g=x26x+6

### Explanation of Solution

Given information:

f(x)=x23x+2 and g(x)=43x

Calculation:

(f+g)(x)=f(x)+g(x)=x23x+2+43x=x26x+6

(b)

To determine

Expert Solution

fg=x22

### Explanation of Solution

Given information:

f(x)=x23x+2 and g(x)=43x

Calculation:

(fg)(x)=f(x)g(x)=x23x+2(43x)=x23x+24+3x=x22

(c)

To determine

### To find: fg if f(x)=x2−3x+2 and g(x)=4−3x

Expert Solution

fg=3x3+13x218x+8

### Explanation of Solution

Given information:

f(x)=x23x+2 and g(x)=43x

Calculation:

(fg)(x)=f(x)×g(x)=(x23x+2)×(43x)=4x212x+83x3+9x26x=3x3+13x218x+8

(d)

To determine

### To find: f/g if f(x)=x2−3x+2 and g(x)=4−3x

Expert Solution

f/g=(x2)(x1)(43x)

### Explanation of Solution

Given information:

f(x)=x23x+2 and g(x)=43x

Calculation:

(f/g)(x)=f(x)g(x)=(x23x+2)(43x)=x22xx+2(43x)=x(x2)1(x2)(43x)=(x2)(x1)43x

(e)

To determine

Expert Solution

fog=9x215x+6

### Explanation of Solution

Given information:

f(x)=x23x+2 and g(x)=43x

Calculation:

(fog)(x)=f(g(x))=(43x)23(43x)+2=16+9x224x12+9x+2=9x215x+6

(f)

To determine

Expert Solution

gof=3x2+9x2

### Explanation of Solution

Given information:

f(x)=x23x+2 and g(x)=43x

Calculation:

(gof)(x)=g(f(x))=43(x23x+2)=43x2+9x6=3x2+9x2

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