2. Graphing Composite Functions
Consider f(x) = √x and g(x) = -x2 + 2x
Determine 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))
3. Ex 1) Consider f(x) = and g(x) = x2 - 4x
Determine f(g(x)) and g(f(x)) and state its domain.
1
x + 3
4. 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))
5. 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
