How do composite functions f(g(x)) work, and why does the order of composition matter?
A composite applies one function to the result of another: f(g(x)) means first do g, then feed its output into f.
A composite applies one function to the result of another: f(g(x)) means first do g, then feed its output into f. The order matters because the operations aren't interchangeable — f(g(x)) and g(f(x)) usually differ. For example with f(x)=x+1 and g(x)=x², f(g(x)) = x²+1 but g(f(x)) = (x+1)². You also need g's outputs to lie in f's domain for the composite to be defined.
Key point
f(g(x)) applies g first, then f; composition is order-sensitive, so f∘g ≠ g∘f in general.
Common mistake
assuming f(g(x)) equals g(f(x)).
Memory tip
inner function first, then outer — and the order changes the result.
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