Michigan Algebra II KHauck

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