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Composite Functions
A composite function applies one function, then feeds the result into another.
Combining Two Functions
Read fg() from the inside out: apply to first, then apply f to whatever produced. This order matters — fg() is usually different from gf().
Example 1 — easy numbers
f() = and () = . Find fg().
- Apply first: () =
- Apply f to that result: f() =
Answer: fg() =
Example 2 — the other order
Using the same f and , find gf().
- Apply f first: f() =
- Apply to that result: () =
Answer: gf() = (different from fg() = )
Example 3 — a general rule
f() = and () = . Find a rule for fg().
- Apply first: () =
- Apply f to that: f() = ()²
Answer: fg() = ()²
Practice
f() = and () = . Find fg().
Your answer
More lessons in Sets and Functions · Next: Inverse Functions · Previous: Evaluating Functions