Function Composition Calculator
Result
Function Composition Calculator — free online calculator.
Formula
- Function Composition Calculator calculates its result from f(x) = ax+b — coefficient a, f(x) = ax+b — constant b, g(x) = ax²+b — coefficient a, g(x) = ax²+b — constant b, x value. It uses the formula f(x)=ax+b · g(x)=ax²+b · (f∘g)(x)=f(g(x)) · (g∘f)(x)=g(f(x)) · f⁻¹(x)=(x−b)/a. Change any input to recalculate the result instantly.
- The main inputs are f(x) = ax+b — coefficient a, f(x) = ax+b — constant b, g(x) = ax²+b — coefficient a, g(x) = ax²+b — constant b, x value. Enter them in the units and format shown in the calculator.
- Keep comparable quantities in compatible units whenever the formula combines or compares them.
- Changing any input above recalculates the result with the same calculation engine used by this page.
Example: Function Composition
- f(x) = ax+b — coefficient a: 2
- f(x) = ax+b — constant b: 3
- g(x) = ax²+b — coefficient a: 1
- g(x) = ax²+b — constant b: 4
- x value: 5
f(x)=a_f x+b_f; g(x)=a_g x²+b_g. Composition evaluated at user x, inverse f⁻¹(x)=(x−b_f)/a_f (a_f must not be zero).
Sample result: Calculating…
Frequently asked questions
What does the Function Composition calculate?
Function Composition Calculator — free online calculator.
Which values should I enter?
Enter f(x) = ax+b — coefficient a, f(x) = ax+b — constant b, g(x) = ax²+b — coefficient a, g(x) = ax²+b — constant b, x value using the units and format shown beside each field.
What formula does this calculator use?
The calculator uses the following relationship: f(x)=ax+b · g(x)=ax²+b · (f∘g)(x)=f(g(x)) · (g∘f)(x)=g(f(x)) · f⁻¹(x)=(x−b)/a.
Why might my result differ from another source?
Results can differ when another source uses different units, rounding rules, conventions or assumptions. Compare the inputs and definitions before comparing results.
Does the result update automatically?
Yes. Changing an input updates the result using the same calculation engine shown on this page.