Composite Function Calculator
Compute (f∘g)(x) = f(g(x)) by evaluating two functions in sequence at a given x value.
About Composite Function Calculator
Function composition (f∘g)(x) means applying g first, then f to the result: f(g(x)). Note that composition is generally not commutative: f(g(x)) ≠ g(f(x)) in most cases. This calculator evaluates both orders for comparison.
Formulas
Composition
(f∘g)(x) = f(g(x))
- f
- Outer function
- g
- Inner function
- x
- Input value
Reverse composition
(g∘f)(x) = g(f(x))
- f
- First function applied
- g
- Second function applied
Worked example
With the default values below, Composite Function Calculator returns (f∘g)(x) = f(g(x)) of 26.00000000. Change any input above and every figure here is recalculated in your browser.
Inputs used
- f(x)
- x^2 + 1
- g(x)
- 2*x - 3
- x value
- 4
Results
- (f∘g)(x) = f(g(x))
- 26.00000000
- (g∘f)(x) = g(f(x))
- 31.00000000
- g(x)
- 5.00000000
- f(x)
- 17.00000000
Step by step
- 1Values used
- 2Composition
- 3Reverse composition
- 4(f∘g)(x) = f(g(x))= 26.00000000
- 5(g∘f)(x) = g(f(x))= 31.00000000
- 6g(x)= 5.00000000
- 7f(x)= 17.00000000
Assumptions and limits
- The result is derived only from the 3 inputs listed above. Anything not among them is not part of the calculation.
- In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
- Figures are rounded for display to 8 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.
How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.
Frequently Asked Questions
Is f(g(x)) the same as g(f(x))?
Not in general. Function composition is not commutative — the order matters. This calculator shows both so you can compare.
What expressions can I use?
Any expression supported by the parser: polynomials, trig functions, logarithms, exponentials, square roots, etc. Use x as the variable.