Michigan Algebra II KHauck

Suppose you are given the two functions f(x) = 2x + 3 and g(x) = –x² + 5. Composition means that you can substitute g(x) as the input of f(x).
This is written as (f o g)(x) or f(g(x)). The value of x is substituted as the input of g(x) and simplified. The result is then substituted as the input of f(x) and simplified again.

Example Given f (x) = 2x + 3 and g (x) = –x² + 5 , find (g o f)(1) .

(g o f)(1) = g( f(1))

Step 1. Substitute the value of x as the input of the innermost function first, in this case f(x).

f (x) = 2x + 3

f (1) = 2(1) + 3

f (1) = 2 + 3

f (1) = 5

Step 2. Use this output as the input of the next innermost function, in this case g(x).

g (5) = -(5)² + 5

g (5) = -25 + 5

g (5) = -20

Therefore, g(f(1)) = -20