Function Notation
Combining Functions
Examples
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