Function composition
Find (f∘g)(x) — substitute g(x) into f(x) and simplify the result.
f(x) =
g(x) =
Function composition
(f∘g)(x) = f(g(x)) — "f of g of x". First apply g, then apply f to the result.
f(x) = x², g(x) = x+1: (f∘g)(x) = f(x+1) = (x+1)² = x² + 2x + 1.
Order matters
(f∘g)(x) ≠ (g∘f)(x) in general. (g∘f)(x) = g(x²) = x² + 1, which is different from x² + 2x + 1.
Domain of composition
The domain of f∘g is all x in the domain of g where g(x) is in the domain of f.
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