Composition of Functions

Remember … A composition of functions means a function of a function.  Work out 1st function.  Plug the answer into the 2nd function.

Suppose f(x) = x2 and g(x) = 2x + 4. Find g  f (7) f  g (2) f  f (3)

Suppose f(x) = x2 and g(x) = 2x + 4. Find g  f (7) Suppose f(x) = x2 and g(x) = 2x + 4. Find g  f (7) 2  49 + 4 = 102 f  g (2) 82 = 64 f  f (3) 92 = 81

Suppose f(x) = x2 and g(x) = 2x + 4. Find g  f  g  f (5)

Suppose f(x) = x2 and g(x) = 2x + 4 Suppose f(x) = x2 and g(x) = 2x + 4. Find g  f  g  f (5) = g  f  g(25) = g  f(54) = g(2916) = 5,836

What is g  f (3) ? g  f (1) ?

What is g  f (3) = y g  f (1) = z

Find the domain and range of g  f

DOMAIN { 1, 2, 3 }

RANGE { x, y, z }

_____ If g(x) =  x – 3 and f(x) = x3 Find the domain and range of f  g(x)

_____ If g(x) =  x – 3 and f(x) = x3 DOMAIN … x – 3 > 0, _____ If g(x) =  x – 3 and f(x) = x3 DOMAIN … x – 3 > 0, so x > 3

_____ If g(x) =  x – 3 and f(x) = x3 RANGE … The answers from g will always be positive, so the answer cubed will be positive too … y > 0