Composite Function Calculator
Composite function calculator works out Value of the combination at x and Combined function from f(x) =, g(x) = and Variable. The default figures on this page give value of the combination at x of 11; change any entry and the result, the working and the sources update together.
Your figures
Updates as you typeHow this is worked out
3 steps
- Substitute g into f: f(g(x)) = 2 * x^2 + 3.
- g(2) = 4.
- f(4) = 11.
Sample tabletable
| x | y |
|---|---|
| -2 | 11 |
| -1 | 5 |
| 0 | 3 |
| 1 | 5 |
| 2 | 11 |
| 3 | 21 |
| 4 | 35 |
Its 5 worked examples are re-run on every release, last on 15 September 2026. What changed
Sources and references
2 sources
What the composite function calculator calculates
Composes two functions f and g in either order, or combines them by sum, difference, product or quotient, then evaluates the result at a chosen input.
How to use this composite function calculator
Enter f(x) =, g(x) =, Variable and Operation. Value of the combination at x updates as you type, and “Use a worked example” loads checked figures you can adjust. Change one figure at a time to see what drives the result.
How the result is worked out
Open “How this is worked out” beside the result for the step-by-step calculation behind Value of the combination at x, Combined function and Operation.
The method follows Stewart, Redlin & Watson, Precalculus: Mathematics for Calculus, section on combining functions and composition and OpenStax College Algebra, section 3.4 "Composition of Functions".
f(x)=2x+3, g(x)=x^2, (f∘g)(2) example
With f(x) =: 2x + 3, g(x) =: x^2, Operation: fog, Evaluate at x =: 2, the calculator returns Value of the combination at x: 11, f(x): 7, g(x): 4. This example is checked against an independent source in the test suite.
What you can compare
Change one input at a time to see how it affects Value of the combination at x, Combined function and Operation. The inputs you can vary are f(x) =, g(x) =, Variable, Operation, Evaluate at x = and Table start.
Results are general information, not financial, tax, legal, medical or engineering advice. Check any decision that matters with a qualified professional.
See something wrong? Report a problem with this calculator
Frequently asked questions
How to do composite functions on a calculator?
Composes two functions f and g in either order, or combines them by sum, difference, product or quotient, then evaluates the result at a chosen input. Open “How this is worked out” beside the result to see each step for your own figures.
How to calculate a composite function?
It needs f(x) =, g(x) =, Variable, Operation, Evaluate at x = and Table start. Nothing else is required, and the figures stay in your browser.
What is the rule for composite functions?
On the figures this page opens with — evaluate at x = 2 — the value of the combination at x is 11. No single number fits everyone: change any figure above and the answer updates as you type, with each step of the arithmetic beside it.
Can you give me an example of a composition function?
Composes two functions f and g in either order, or combines them by sum, difference, product or quotient, then evaluates the result at a chosen input. On the figures this page opens with — evaluate at x = 2 — the value of the combination at x is 11. Put your own figures in their place and the working updates beside the result.
What information do I need for the composite function calculator?
You need f(x) =, g(x) =, Variable, Operation, Evaluate at x =, Table start, Table step and Table rows. The page opens with default figures that give value of the combination at x of 11, so you can see the scale before entering your own.
What does this composite function calculator show?
It shows Value of the combination at x, Combined function, Operation, f(x), g(x), Inner function value, Sample table and f∘g equals g∘f at this point, with the working and any warnings for your entries.