# ADD SUBTRACT MULTIPLY AND DIVIDE FUNCTIONS

## Function Operations

(f + g)(x) = f(x) + g(x)

Subtraction :

(f - g)(x) = f(x) - g(x)

Multiplication :

(f  g)(x) = f(x)  g(x)

Division:

(f/g)(x) = f(x)/g(x), g(x) ≠ 0

Example 1 :

What is (f + g)(x) ?

f(x) = -x + 5 and g(x) = 3x + 2

Solution :

(f + g)(x) = f(x) + g(x)

-x + 5 + 3x + 2

2x + 7

Example 2 :

What is (f - g)(x) ?

f(x) = 2x2 + 5x - 7 and g(x) = -4x2 + 2x + 3

Solution :

(f - g)(x) = f(x) - g(x)

= 2x2 + 5x - 7 -(-4x2 + 2x + 3)

= 2x2 + 5x - 7 + 4x2 - 2x - 3

= 6x2 + 3x - 10

Example 3 :

What is (f + g - h)(x) ?

f(x) = 4x - 7, g(x) = 3x + 18 and h(x) = -5x + 2

Solution :

(f + g - h)(x) = f(x) + g(x) - h(x)

= (4x - 7) + (3x + 18) - (-5x + 2)

4x - 7 + 3x + 18 + 5x - 2

Combine the like terms.

= 12x + 9

Example 4 :

What is (f ⋅ g)(x) ?

f(x) = 3x2 and g(x) = 5x + 2

Solution :

(f  g)(x) = f(x)g(x)

= (3x2)(5x + 2)

= 15x3 + 6x2

Example 5 :

What is (f/g)(x) ?

f(x) = (5x + 20) and g(x)(7x + 28)

Solution :

(f/g)(x) = f(x)/g(x)

= (5x + 20)/(7x + 28)

= 5(x + 4)/7(x + 4)

= 5/7

Example 6 :

What is (f ⋅ g ⋅ h)(x) ?

f(x) = 6x - 8, g(x) = x/2 and h(x) = 4x

Solution :

(f ⋅ g ⋅ h)(x) = f(x)g(x)h(x)

= (6x - 8)(x/2)(4x)

= (6x - 8)(x)(2x)

= (6x - 8)(2x2)

= 12x3 - 16x2

Example 7 :

If f(x) = 3x + 2 and g(y) = 5y + 1, evaluate f(2)g(4).

Solution :

f(x)g(y) = (3x + 2)(5y + 1)

Substitute x = 2 and y = 4.

f(x)g(y) = (3x + 2)(5y + 1)

Substitute x =2 and y = 4

f(2)g(4) = [3(2) + 2][5(4) + 1]

= (6 + 2)(20 + 1)

= (8)(21)

= 168

Example 8 :

What is (f/g)(x) ?

f(x) = xy + 3x - 2y - 6 and g(x) = y2 + y - 6

Solution :

(f/g)(x) = f(x)/g(x)

= (xy + 3x - 2y - 6)/(y2 + y - 6)

= [x(y + 3) - 2(y + 3)]/[(y + 3)(y - 2)]

= [(y + 3)(x - 2)]/[(y + 3)(y - 2)]

= (x - 2)/(y - 2)

Example 9 :

What is (f ⋅ g)(x) ?

f(x) = x2 - 4 and g(x) = x2 + 4

Solution :

(f ⋅ g)(x) = f(x)g(x)

= (x2 + 4)(x2 + 4)

= (x2)2 - 42

= x4 - 16

Example 10 :

What is (f/g)(x) ?

f(x) = ax - ay + bx - by and g(x) = ax - ay - bx + by

Solution :

(f/g)(x) = f(x)/g(x)

= (ax - ay + bx - by)/(ax - ay - bx + by)

= [a(x - y) + b(x - y)]/[a(x - y) - b(x - b)]

= [(x - y)(a + b)]/[(x - y)(a - b)]

= (a + b)/(a - b)

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