Operations on Functions

Concept sheet | Mathematics
Definition

Operations on functions include addition, subtraction, multiplication, division, and the composition of functions.

Given functions |f(x)| and |g(x),| each operation is written as follows.

Addition

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

Subtraction

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

Multiplication

|(f\times g)(x)=f(x) \times g(x)|

Division

|(f\div g)(x) = f(x) \div g(x)|

Composition

|(f\circ g)(x)=f\big(g(x)\big)|

Important!

Make sure to carefully identify the domain of the function obtained after doing an operation.