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 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 2 = 4 + 1= 5

5 5 5= 25 + 30 - 27= 28

Let’s try the same problem again, only thistime, we’ll let the calculator do all the work!

f(x) = x 2 + 6 x - 27 and g(x) = x 2 + 1Evaluate f(g(2))

Enter g(x) into Y1 and enter f(x) into Y2 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 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)) = x4 + 8x2 - 20

x x = x2 + 1

x2 + 1 x2 + 1 x2 + 1

= x4 + 2x2 + 1 + 6x2 + 6 - 27

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)) = 18x2 – 69x + 67

x x = 3x - 5

3x - 5 3x - 5 3x - 5

= 2(9x2 - 30x + 25) – 9x + 15 + 2