A composite function applies one function and then another. fg(x) means do g first, then put the result into f. The function nearest to x acts first.
If f(x) = 3x − 1 and g(x) = −4x − 6, then fg(2) = f(g(2)) = f(−14) = −43. To find fg(x) as an expression, put the whole of g(x) into f: fg(x) = 3(−4x − 6) − 1 = −12x − 19. Usually fg(x) and gf(x) are different.
Worked example
f(x) = 4x − 5, g(x) = 3x + 2. Find gf(−3).
- f acts first: f(−3) = −12 − 5 = −17.
- Then g: g(−17) = −51 + 2 = −49.
Answer:−49
Key words
- composite function
- one function applied after another
- fg(x)
- g first, then f
- domain
- the inputs a function accepts
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Common Core-referenced: HSF-BF.A.1c