Function Composition Calculator
Enter f and g as coefficients from the highest power down, then a value of x.
This result is an estimate only. Double-check important figures before relying on them.
How it is calculated
- f(g(x)): replace every x in f with the whole expression g(x), then expand
- g(f(x)): the same, the other way round
To multiply two polynomials, use the polynomial multiplication calculator.
Worked example
f(x) = x², g(x) = x + 1:
- f(g(x)) = x² + 2x + 1
- g(f(x)) = x² + 1
- At x = 2: 9 and 5
Why your number may differ
The expansion is exact for whole coefficients and rounded to 6 places otherwise.
Frequently asked questions
What is function composition?
Feeding the output of one function into another. f(g(x)) means apply g first, then f.
Is f(g(x)) the same as g(f(x))?
Usually not. The order matters, as the two results here show.
Can I compose non-polynomial functions?
Not here. This tool handles polynomials entered by their coefficients.