Function Composition Calculator
Calculate function compositions (f∘g)(x) = f(g(x)) and explore properties.
Define Functions
Supported: +, -, *, /, ^, sqrt, sin, cos, tan, log, exp, abs
Compositions at x = 2
(f ∘ g)(x) = f(g(x)):
9
(g ∘ f)(x) = g(f(x)):
25
Step by Step
1. g(2) = 4
2. f(4) = 9
Therefore (f ∘ g)(2) = 9
1. f(2) = 5
2. g(5) = 25
Therefore (g ∘ f)(2) = 25
Commutative at x = 2?NO
Function composition is generally NOT commutative
Evaluation Table
| x | f(x) | g(x) | (f∘g)(x) | (g∘f)(x) |
|---|---|---|---|---|
| -2 | -3 | 4 | 9 | 9 |
| -1 | -1 | 1 | 3 | 1 |
| 0 | 1 | 0 | 1 | 1 |
| 1 | 3 | 1 | 3 | 9 |
| 2 | 5 | 4 | 9 | 25 |
| 3 | 7 | 9 | 19 | 49 |