Problem of the Day

Graphing Composite Functions

Consider f(x) = √x and g(x) = -x2 + 2xDetermine f(g(x)) and g(f(x))

To find the domain of f(g(x)) you must consider the restrictions on the domain of g(x) and the new restrictions for (f(g(x))

Ex 1) Consider f(x) = and g(x) = x2 - 4x Determine f(g(x)) and g(f(x)) and state its domain.

1x + 3

Ex 2) Let f(x) = x + 1 and g(x) = x2. Sketch a graph of each composite function below and state its domain and range.a) y = f(g(x))b) y = g(f(x))c) y = f(f(x))d) y = g(g(x))

Ex 3) Determine possible functions f(x) and g(x) so that: a) f(g(x)) = (x - 2)2 b) f(g(x)) = √x + 3 c) f(g(x)) = x2 + 4x + 3