Operations Of Functions

We can evaluate two functions together if we apply the operations of mathematics.

Let f and g be the function.

Addition

f(x) = 2x^2 - 5x + 12

g(x) = 3x^2 + 7x -10

formula: (f + g) (x) = f(x) + g(x)

(f + g) (x) = 2x^2 - 5x + 12 + 3x^2 + 7x -10

(f + g) (x) = 5x^2 + 2x - 2

Subtraction

f(x) = 2x^2 - 5x + 12

g(x) = 3x^2 + 7x -10

formula: (f - g) (x) = f(x) + (-g(x))

(f + g) (x) = 2x^2 - 5x + 12 - (3x^2 + 7x -10)

(f + g) (x) = 2x^2 - 5x + 12 + (-3x^2 - 7x + 10)

(f + g) (x) = 2x^2 - 12x + 22

Multiplication f(x) = 2x + 5

g(x) = x^2 - 1

formula: (f x g) (x) = (f(x)) (g(x))

(f x g) (x) = (2x + 5) (x^2 - 1)

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

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

Division f(x) = 6x^2 - x -12

g(x) = 2x - 3

formula: (f/g) (x) = f(x)/g(x)

(f/g) (x) = 6x^2 - x -12/2x - 3

(f/g) (x) = (2x - 3) (3x + 4)/2x - 3

cancel 2x - 3 since there are both like terms

(f/g) (x) = 3x + 4

More References:

Addition:

Subtraction:

Multiplication:

Division: