About the Function Composition Calculator

Function composition chains operations: (f∘g)(x) = f(g(x)) means "run g on x, then run f on the output." It is the mathematical version of a pipeline — the inner function feeds the outer one. For f(x) = 2x + 1 and g(x) = x² − 3, the composition (f∘g)(x) = 2(x² − 3) + 1 = 2x² − 5, so at x = 2 the value is 3.

Why order matters

Composition is not commutative: reversing the order gives g(f(x)) = (2x + 1)² − 3, a completely different function. This is why the calculator shows both directions and a value table — watching f(g(x)) diverge from g(f(x)) across inputs makes the non-commutativity concrete. The parser accepts simple polynomials without any eval, so expressions like 3x^2 + 2x − 5 are safe to enter.