Calculator Inputs
Enter two functions of x, choose the evaluation point, and define the plotting range. Supported functions: sin, cos, tan, asin, acos, atan, sqrt, abs, log, ln, exp, floor, ceil.
The calculator accepts explicit multiplication such as 2*x and also supports common implicit forms like 2x and 3(x+1).
Example Data Table
Example functions: f(x) = x^2 + 1 and g(x) = 2x - 3.
| x | f(x) | g(x) | f(g(x)) | g(f(x)) |
|---|---|---|---|---|
| 0 | 1 | -3 | 10 | -1 |
| 1 | 2 | -1 | 2 | 1 |
| 2 | 5 | 1 | 2 | 7 |
| 3 | 10 | 3 | 10 | 19 |
Formula Used
How to Use This Calculator
- Enter the first function in the f(x) field.
- Enter the second function in the g(x) field.
- Provide the x-value where you want numeric results.
- Choose graph start, graph end, and graph step values.
- Click the calculate button to see values above the form.
- Review the graph, substituted expressions, and generated table.
- Use the export buttons to download the computed dataset.
Frequently Asked Questions
1) What is a composite function?
A composite function applies one function to the output of another. For example, f(g(x)) first evaluates g(x), then places that result inside f. The order matters and usually changes the answer.
2) Why are f(g(x)) and g(f(x)) different?
Function composition is not usually commutative. Changing the order changes which expression is evaluated first. That change often produces different substituted forms, different numeric outputs, and different graph shapes.
3) What input syntax does this calculator support?
You can use x, parentheses, powers, and common functions like sin, cos, sqrt, log, ln, and exp. Explicit multiplication such as 2*x is supported, and common implicit multiplication forms are also accepted.
4) What happens when a value is undefined?
If a function is undefined at a selected point, the calculator shows Undefined for that value. On the graph, undefined points are left blank so the plot does not draw invalid connections.
5) What does the graph show?
The graph compares four curves: f(x), g(x), f(g(x)), and g(f(x)). This helps you study how composition changes outputs across the chosen interval and how the order affects curve behavior.
6) What do the CSV and PDF downloads contain?
Both exports use the generated table from your selected graph range. They include x, f(x), g(x), f(g(x)), and g(f(x)) values, making it easier to save, review, or share your work.
7) Can I use negative, decimal, or large values?
Yes. The calculator accepts negative and decimal inputs for the evaluation point and graph range. For very large ranges, use a larger step size to keep the graph and exported table manageable.
8) How do I choose a good graph step?
A smaller step gives smoother detail but creates more points. A larger step generates fewer points and faster output. Start with 0.5 or 1, then adjust based on the function’s complexity.