Function Notation: Examples

Function Notation

Example 1

Given f(x) = 3x +5 and g(x) = 5x - 2 find (f + g)(x)

Step 1. Substitute the functions in (f + g)(x) = f(x) + g(x)

(3x +5) + (5x - 2)

Step 2. Combine like terms to simplify.

(f + g)(x) = 8x + 3

Example 2

Given h(x) = 3x + 4 and k(x) = 1 - 2x find (h - k)(x).

Step 1. Substitute the functions in the difference rule.

(3x + 4 ) - (1 - 2x)

Step 2. Use Distributive Property to eliminate the parentheses.

3x + 4 -1 + 2x

Step 3. Combine like terms to simplify.

(h - k)(x) = 5x + 3