2. Composite Functions f(g(x)) = f o g(x) 1) Start with inside function first. Steps of evaluating composite functions. Evaluate g(x) 2) Use your result as the input for the outside function. Evaluate g(x) in f(x)

3. f(x) = x 2 + 6 x - 27 and g(x) = x 2 + 1 Evaluate f(g(2)) 1) g( ) = ( ) 2 + 1 2) f( ) = ( ) 2 + 6 ( ) - 27 f(g(2)) = 28 2 = 4 + 1= 5 5 5 5 = 25 + 30 - 27 = 28

4. Let’s try the same problem again, only this time, we’ll let the calculator do all the work! f(x) = x 2 + 6 x - 27 and g(x) = x 2 + 1 Evaluate f(g(2)) Enter g(x) into Y 1 and enter f(x) into Y 2 Press [2nd] [QUIT] to bring up home screen Press [VARS] [Y-Vars] [1] [1] (2) to evaluate g(2) Press [VARS] [Y-Vars] [1] [2] (5) to evaluate f(5)

5. Oh my goodness! It’s the same answer as before! That was easy

6. f(x) = x 2 + 6 x - 27 and g(x) = x 2 + 1 Evaluate f(g(x)) 1) g( ) = ( ) 2 + 1 2) f( ) = ( ) 2 + 6 ( ) - 27 f(g(x)) = x 4 + 8x 2 - 20 x = x 2 + 1 x 2 + 1 x 2 + 1 x 2 + 1 = x 4 + 2x 2 + 1 + 6x 2 + 6 - 27

7. f(x) = 2 x 2 - 3 x + 2 and g(x) = 3 x - 5 Evaluate f(g(x)) 1) g( ) = 3( ) - 5 2) f( ) = 2( ) 2 - 3 ( ) +2 f(g(x)) = 18x 2 – 69x + 67 x = 3x - 5 3x - 5 3x - 5 3x - 5 = 2(9x 2 - 30x + 25) – 9x + 15 + 2