फलन संयोजन कैलकुलेटर
f(g(x)) · g(f(x)) · f(f(x)) · Step-by-Step · Domain · Graph
Compose two functions symbolically and numerically. See the substitution steps, domain restrictions, and a live graph of all three composed functions.
त्वरित उदाहरण
Syntax: Use ^ for powers, * for multiply, sqrt(x), abs(x), log(x), ln(x), sin(x), cos(x), tan(x), exp(x)
चरण-दर-चरण प्रतिस्थापन — (f∘g)(x)
संयुक्त फलनों का प्रांत (Domain)
ग्राफ़
Graph range: x ∈ [−6, 6]. Values outside [−20, 20] are clipped for readability.
Notation & Properties Reference
f∘g notation
(f∘g)(x) = f(g(x))
Apply g first, then f. Read: "f composed with g" or "f of g of x".
g∘f notation
(g∘f)(x) = g(f(x))
Apply f first, then g. Order is reversed from f∘g.
Commutativity
f∘g ≠ g∘f (generally)
Composition is NOT commutative. Order matters.
Associativity
(f∘g)∘h = f∘(g∘h)
Composition IS associative. Grouping doesn't change the result.
Inverse & Identity
(f∘f⁻¹)(x) = x
Composing a function with its inverse gives the identity function.
Domain Rule
Dom(f∘g) = {x ∈ Dom(g) : g(x) ∈ Dom(f)}
x must be valid in g AND g(x) must be valid in f.
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