How to use this calculator
Composition means using the output of one function as the input of another. It is not the same as multiplication, and reversing the order generally changes the result. This tool substitutes entire polynomials, expands the powers, combines like terms, and evaluates the resulting polynomial at your selected point.
The method
Enter the values in the labeled fields, check the units or selected mode, and choose Calculate. The result includes the applicable working and a breakdown or visual when useful. Change an input and calculate again to update the result.
f(x) coefficients: 1, 0, 1 g(x) coefficients: 2, 3 Composition: f(g(x)) Evaluate at x: 2
Composite polynomial: 4x^2 + 12x + 10
f(g(x)) evaluated at x = 2 gives 50.
Scope and limitations
Polynomial inputs only, each of degree 4 or less. The resulting degree can be as high as 16. All polynomial compositions have the full real domain; non-polynomial domain restrictions are outside this tool.
Common questions
Is f(g(x)) the same as f(x)g(x)?
No. Composition substitutes one function into the other. Multiplication simply multiplies their two outputs.
Why does switching the order change the answer?
The outer function receives a different input after the switch. Composition is generally not commutative.
References & further reading
External references provide background, not an endorsement of this implementation. See our methodology for numerical conventions and limitations.