Calculate f(g(x)) and g(f(x)) with step-by-step solutions. Enter two functions and get the composed result instantly.
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Function composition combines two functions by plugging one into the other. f(g(x)) means "first apply g, then apply f to the result." It's written as (f ∘ g)(x).
Order matters! f(g(x)) applies g first, then f. g(f(x)) applies f first, then g. These usually give different results.
Replace every x in f(x) with the entire expression g(x). Then simplify by expanding and combining like terms.
To find f(g(2)): first compute g(2), then plug that result into f. For example, if g(x) = 2x+1, then g(2) = 5, and f(5) gives your answer.
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InstallTo find f(g(x)): (1) Write out f(x) and g(x), (2) Wherever you see x in f(x), replace it with the entire expression for g(x), (3) Expand and simplify. For example, if f(x) = x² + 1 and g(x) = 2x + 3, then f(g(x)) = (2x+3)² + 1 = 4x² + 12x + 10.
No. Function composition is not commutative. f(g(x)) and g(f(x)) usually give different results. For example, if f(x) = x² and g(x) = x + 1, then f(g(x)) = (x+1)² = x² + 2x + 1, but g(f(x)) = x² + 1.
The domain of f(g(x)) is all x values in the domain of g where g(x) is in the domain of f. You must check both conditions.
First compute g at that value, then plug the result into f. For f(g(2)) with f(x) = x² and g(x) = 3x: g(2) = 6, then f(6) = 36.