Composition of Functions
Symbolic Composition
Example 2
Given f(x) = 2x + 3 and g(x) = –x2 + 5 , find (g o f)(x) .
(g o f)(x) = g(f(x))
= g(2x + 3)
Step 1. Rewrite the outer-function, leaving empty parentheses for the input expression.
g( )= -1( )2 + 5 ... setting up to insert the input formula
Step 2. Insert the function f(x) into the parentheses as the input expression.
g(2x +3)= -1(2x + 3)2 + 5
Step 3. Simplify the right side of the equals sign.
g(2x + 3)= –1(4x2 +12x + 9) + 5
g(f(x))= –4x2 – 12x – 4