High School Function Composition Calculator
Compute f(g(x)) and g(f(x)) at specific points and visualize the result.
Final Result
Step-by-Step Evaluation
Composition Graph
How to use the Function Composition Calculator
In algebra, function composition involves applying one function to the results of another. The notation (f ∘ g)(x) means f(g(x)). You can think of this as a two-step machine process:
- Input: Start with a value x.
- Inner Function: Plug x into the inner function g to get an output value. Let’s call this u.
- Outer Function: Take that result u and plug it into the outer function f.
- Output: The final result is f(u), which is equal to f(g(x)).
Why use a Function Composition Calculator?
Calculating composites manually can be tricky, especially keeping track of variables. For example, if f(x) = 2x + 3 and g(x) = x², finding f(g(2)) requires order: first 2² = 4, then 2(4) + 3 = 11. However, swapping them to find g(f(2)) gives a completely different result: 2(2)+3 = 7, then 7² = 49. This tool helps verify these steps and visualizes how the composite function behaves compared to its components.
Domain Considerations
Remember that for a composite function f(g(x)) to exist, the output of g(x) must be in the domain of f(x). For example, if f(x) = √x, you cannot plug in a negative result from g(x).
FAQ
No. In general, f(g(x)) ≠g(f(x)). Order matters significantly in composition.
Use the caret symbol (^). For example, type x^2 for x squared.
Yes! You can use sin(x), cos(x), tan(x), sqrt(x), log(x), and more.
NaN stands for “Not a Number”. This usually happens if you calculate something undefined, like dividing by zero or taking the square root of a negative number.