How to Use the Composite Function Calculator
Enter the coefficients for two linear functions, f(x)=ax+b and g(x)=cx+d, along with a value of x, and this calculator finds f(g(x)) and g(f(x)) automatically. Composition means feeding the output of one function into another, written as fâg and read as "f of g of x."
The order matters: evaluate the inner function first. To find f(g(x)), first substitute x into g(x) to get its value, then plug that result into f(x). For example, if f(x)=2x+1, g(x)=3x-2, and x=4, then g(4)=3Ă4-2=10, and f(10)=2Ă10+1=21, so f(g(4))=21.
Keep in mind that function composition is not commutative â f(g(x)) and g(f(x)) generally give different results. That's why this calculator computes both directions so you can compare them directly. It's a useful tool for high school and college function units, and for understanding the function-pipeline pattern common in programming.
Frequently Asked Questions
First substitute x into g(x) to find the value of g(x). Then substitute that result into f(x) to get f(g(x)). In short: evaluate the inner function first, then feed its output into the outer function.
No. Function composition is generally not commutative, so f(g(x)) and g(f(x)) are different functions and usually produce different values.