Operations on functions

This lesson will teach you how to perform operations on functions. Basically, you can add, subtract, multiply, and divide functions. Let f and g be functions.

Addition

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

Example

Find f + g if  f(x) = 2x - 7 and g(x) = 5x + 8

(f + g)(x)   =   f(x) + g(x)

                 = 2x - 7 + 5x + 8

                 = 2x + 5x + - 7 + 8
 
                = 7x + 1


Subtraction

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

Example

Find f - g if  f(x) = 3x + 9 and g(x) = 6x - 3

(f - g)(x)   =   f(x) - g(x)

                 = 3x + 9  -  (6x - 3)

                 = 3x + 9  - 6x - - 3
  
                 = 3x + 9 - 6x + 3

                 = 3x - 6x + 9 + 3

                = -3x + 12

Multiplication

( f × g )(x) = f(x) × g(x)

Example

Find f × g if f(x) = x + 1 and g(x) = x + 5

(f × g)(x) = f(x) × g(x)

= (x + 1) × (x + 5)

= x × x + x × 5 + 1 × x + 1 × 5

= x2 + 5x + 1x + 5

x2 + 6x + 5


Division

( f / g )(x) = f(x) / g(x)     with g(x) ≠ 0

Example

Find f / g if f(x) = x2 - 1 and g(x) = x + 1

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

= (x2 - 1) / (x + 1)    with x + 1 ≠ 0

= [(x - 1) × (x + 1)] / x + 1    with x + 1 ≠ 0

= x - 1     with x + 1 ≠ 0

= x - 1     with x ≠ -1

Recent Articles

  1. How to Write an Inequality

    Dec 12, 19 07:51 AM

    Learn how to write an inequality quickly with this easy to follow math lesson.

    Read More

New math lessons

Your email is safe with us. We will only use it to inform you about new math lessons.

                                 Follow me on Pinterest

Real Life Math Skills

Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.