2.7.A.1Concept
If f and g are functions, the composite function f∘g maps a set of input values to a set of output values such that the output values of g are used as input values of f. For this reason, the domain of the composite function is restricted to those input values of g for which the corresponding output value is in the domain of f. (f∘g)(x) can also be represented as f(g(x)).
ExampleEvaluate f(g(x))1 / 3
Let f(x) = x² + 1 and g(x) = 3x − 2. Find (f∘g)(2) and (f∘g)(−1).
Try it on paper first, then reveal each step to check your work.
Step 1 — Inner first
(f∘g)(2) = f(g(2)). Start inside: g(2) = 3(2) − 2 = 4.