Function Composition Calculator
How It Works
This function composition calculator uses established formulas to provide accurate results.
The basic rule:
- (f ∘ g)(x) = f(g(x))
- (g ∘ f)(x) = g(f(x))
- In general, f(g(x)) ≠ g(f(x))
Results are estimates. Consult a professional for critical decisions.
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Explore Allday Everyday Math →Frequently Asked Questions
What is function composition?
Function composition means plugging one function into another. f(g(x)) means first evaluate g(x), then plug that result into f. It is written as (f ∘ g)(x).
Does order matter in composition?
Yes! f(g(x)) is generally different from g(f(x)). Composition is not commutative. Always pay attention to which function is the outer one and which is the inner one.
How do I evaluate f(g(x))?
Step 1: Calculate g(x) for your x-value. Step 2: Take that answer and plug it into f. For example, if g(2) = 7 and f(7) = 15, then f(g(2)) = 15.