Understanding Function Composition

Function composition is fundamental in mathematics and computer science, allowing complex transformations by combining simpler functions. It's used in engineering for system modeling, in economics for chained transformations, and in machine learning for building neural networks.

Step-by-Step Guide

Enter your outer function f(x) using standard math notation
Enter your inner function g(x)
Input the x value you want to evaluate
The calculator computes g(x) first, then applies f to that result

Examples

If f(x) = x² and g(x) = 2x + 1, then f(g(3)) = (2×3 + 1)² = 49
If f(x) = √x and g(x) = x - 4, then f(g(8)) = √(8-4) = 2

Common Functions Reference

Function	Notation
Square	x^2
Square Root	sqrt(x)
Exponential	e^x

Warning: Avoid division by zero and negative inputs for even roots. Check your function domains before composition.

Composite Function Calculator

Result

Understanding Function Composition

Step-by-Step Guide

Examples

Common Functions Reference

Function Notation Converter

Frequently Asked Questions

What is function composition?

Can I use trigonometric functions?

Why is my result showing "Error"?

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Composite Function Calculator - Compute f of g of x

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