The document provides examples of evaluating composite functions. It gives the steps to find (f ◦ g)(x) by substituting the expression for g(x) into f(x) and simplifying. Examples are provided of finding (f ◦ g)(x) and (g ◦ f)(x) for various functions f(x) and g(x), as well as evaluating composite functions at given values.

2. Ex 1) If f(x) = x + 1 and g(x) = 2x, find (f ◦ g)(x).
Steps:
1) Write the expression for
the function of g (2x) in the
g(x) 'spot' in the composition
2) Now substitute this
expression (2x) into function f
in the x 'spot'
3) Simplify (if necessary)

3. Ex 2) Given f(x) = 5x and g(x) = x2 + 1, find
a) (f ◦ g)(x)
b) (g ◦ f)(x)
Notice that (f ◦ g)(x) and (g ◦ f)(x) do not
necessarily have the same answer.

4. Ex 3) Given f(x) = x2 and g(x) = x + 3, find
a) f(g(x))
b) g(f(x))
c) f(f(x))
d) g(g(x))

5. Ex 4) If f(x) = 4x, g(x) = x + 6, and h(x) = x2, find
a) f(g(3))
b) g(h(-2))
c) h(h(2))
Two options possible