HOW TO MULTIPLY AND DIVIDING FUNCTIONS

Problem 1 :

If f(x) = 2x - 6 and g(x) = x² - 5x + 6, find f(x)/g(x).

Solution:

Problem 2 :

If f(x) = -7x + 2 and g(x) = x³ + x², find (g · f)(x).

Solution:

(g · f)(x) = g(x)·f(x)

(g · f)(x) = (x³ + x²) · (-7x + 2)

= -7x⁴ + 2x³ - 7x³ + 2x²

= -7x⁴ - 5x³ + 2x²

Problem 3 :

If f(x) = 4x - 8 and g(x) = -x² + 6x - 8; find the following.

i) f(x) · g(x)     ii) (g/f)(x)

Solution:

f(x) · g(x) = (4x - 8) (-x² + 6x - 8)

= -4x³ + 24x² - 32x + 8x² - 48x + 64

= -4x³ + 32x² - 80x + 64

f(x) · g(x) = -4(x³ - 8x² + 20x + 16)

ii) (g/f)(x)

Problem 4 :

If f(x) = 10x + 3 and g(x) = x + 15, find (f/g)(6).

Solution:

Problem 5 :

If f(x) = -3x - 9 and g(x) = 5x² + 1, find g(-3) · f(-3).

Solution:

g(x) · f(x) = (5x² + 1)·(-3x - 9)

g(-3) · f(-3) = (5(-3)² + 1)·(-3(-3) - 9)

= (46)·(0)

= 0

Problem 6 :

If f(x) = 5 - x and g(x) = 12 + 7x²; find the following.

i) (f · g)(-2)      ii) g(4)/f(4)

Solution:

(f · g)(x) = (5 - x) · (12 + 7x²)

(f · g)(-2) = (5 - (-2)) · (12 + 7(-2)²)

= (7) (40)

= 280

ii) g(4)/f(4)

Solution:

Problem 7 :

f(x) = 2x³ - 5x² and g(x) = 2x - 1

Find (f  · g)(x).

Solution:

(f  · g)(x) = f(x)·g(x)

= (2x³ - 5x²) · (2x - 1)

= 4x⁴ - 2x³ - 10x³ + 5x²

= 4x⁴ - 12x³ + 5x²

Problem 8 :

g(t) = t² + 3 and h(t) = 4t - 3

Find (g · h)(-1)

Solution:

(g · h)(t) = (t² + 3) · (4t - 3) 

(g · h)(-1) = ((-1)² + 3) · (4(-1) - 3)

= (1 + 3) · (-4 - 3)

= 4 · (-7)

= -28

Problem 9 :

g(a) = -3a² - a and h(a) = -2a - 4

Find (g/h)(a)

Solution:

Problem 10 :

f(x) = 3x - 1 and g(x) = x² - x

Find (f/g)(x)

Solution: