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)

f(x) = x x - 27 and g(x) = x Evaluate f(g(2)) 1) g( ) = ( ) ) f( ) = ( ) ( ) - 27 f(g(2)) = 28 2 = 4 + 1= = = 28

Let’s try the same problem again, only this time, we’ll let the calculator do all the work! f(x) = x x - 27 and g(x) = x 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)

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

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

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