Basic Operations

Dividing Functions

To divide functions, put the first function as the numerator of a fraction and the second function as the denominator of a fraction. Simplify if possible. Always define your function; division by zero is not defined. Therefore, values that would create a zero in the denominator are not allowed. This concept will be addressed in more detail in the rational functions unit.

Example 1 Given f(x) = 3x – 5 and g(x) = 6x + 5, find f(x) ÷ g(x).

Step 1. Put the functions in fraction form.

 

Step 2. Try to simplify the new expression.

This expression is already simplified.

 

Step 3. Be sure your expression is defined.

Since division by zero is undefined, .

Therefore, f(x) ÷ g(x) = ; when .