Operations on Functions: Adding and Subtracting Functions

Operations on Functions: Adding and Subtracting Functions

Operations on Functions: Adding and Subtracting Functions 150 150 SchoolTutoring Academy

A function is a relation that assigns to each input value exactly one output value. Like numbers and polynomials we can add, subtract, multiply and divide functions which results into a new function. Below are the rules to perform these operations on functions.

Let f(x) and g(x) be two functions:

Addition

We can add two functions as:

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

Example:

f(x) = 2x2 + 3x – 4 and g(x) = 2x + 3

(f + g)(x) = (2x2 + 3x – 4) + (2x + 3)

= 2x2 + 5x – 1

Subtraction

We can subtract two functions as:

(f – g)(x) = f(x) – g(x)

Example:

f(x) = 2x2 + 3x – 4 and g(x) = 2x + 3

(f – g)(x) = (2x2 + 3x – 4) – (2x + 3)

= 2x2 + x – 7

Multiplication

(f•g)(x) = f(x)•g(x)

Example:

f(x) = 3x – 5 and g(x) = x

(f•g)(x) = (3x – 5)•(x)

= 3x2 – 5x

Division

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

Example:

f(x) = 3x2 + 4x – 3 and g(x) = x

(f/g)(x) = (3x2 + 4x – 3)/x

= 3x + 4 – 3/x

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