1. = + 1 x x2 - 4 x2 - 4 1 1 x x2 x g(x) = f(x) = x2 - 4 g(f(x))
Write down g(x)
with brackets for x 1
x2 - 4 x
x2 - 4
g(x) = 1
( )
Domain
x-axis values
Input
inside bracket put f(x)
Range
y-axis values
Output
g(f(x)) = 1
x2 - 4
A complex function made up of 2 or more simpler functions
Similar to composite Area
Restriction
x2 - 4 ≠ 0
Composite Functions
(x – 2)(x + 2) ≠ 0 = +
x ≠ 2
x ≠ -2
f(g(x)) =
g(x) = 1 x
f(x) = x2 - 4
f(g(x))
Write down f(x)
with brackets for x
- 4 1 x2 1 x x
f(x) =
( )2 - 4
inside bracket put g(x) 1 x 2
- 4 = 1 x2
- 4
f(g(x)) =
Domain
x-axis values
Input
Range
y-axis values
Output
Restriction
x2 ≠ 0