Maths · Algebra and graphs. The idea in plain words, the rules to remember, the mistake to avoid and a worked example, written and checked by Mega Lecture.
A function is a rule that changes each input into one output. f(x) = 3x − 5 means "multiply by 3, then subtract 5". To find f(2), replace every x with 2. The set of allowed inputs is the domain and the set of outputs is the range.
The inverse function f−1(x) undoes f. It takes an output back to its input.
A composite function uses one function after another. fg(x) means f(g(x)): work out g first, then put the result into f. The order matters, so fg(x) and gf(x) are usually different.
fg(x) is not f(x) × g(x), and it is not f first. The function nearest to x is done first, so in fg(x) you do g and then f.
Answer: fg(x) = 4x + 17 and f⁻¹(x) = (x + 3)/4
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