Function Composition Calculator
Function Composition Calculator
Function composition means feeding the output of one function directly into another, written f(g(x)) — a concept that comes up constantly whenever a real-world process involves multiple chained steps, like converting units before applying a formula. Enter an outer function, an inner function, and a value of x, and this calculator evaluates the inner function first, then feeds that result into the outer one. Order matters here: f(g(x)) generally gives a different answer than g(f(x)), since you're plugging values into different functions depending on which comes first.
- Function composition means feeding the output of one function into another, written f(g(x)) — you always evaluate the inner function g(x) first, then use that result as the input to f.
- The order matters: f(g(x)) is generally not the same as g(f(x)), since evaluating them in the opposite order plugs values into different functions.
- Composition is common in describing chained processes, like converting units and then applying a formula, or applying multiple transformations to data in sequence.
How do I compute a composed function f(g(x))?
First substitute your value of x into g(x) and simplify to get a number. Then substitute that resulting number into f(x) in place of x, and simplify again.
What is f(g(3)) if f(x) = 2x + 1 and g(x) = x²?
First g(3) = 3² = 9, then f(9) = 2(9) + 1 = 19.
Function Composition Calculator
Function composition means feeding the output of one function directly into another, written f(g(x)) — a concept that comes up constantly whenever a real-world process involves multiple chained steps, like converting units before applying a formula. Enter an outer function, an inner function, and a value of x, and this calculator evaluates the inner function first, then feeds that result into the outer one. Order matters here: f(g(x)) generally gives a different answer than g(f(x)), since you're plugging values into different functions depending on which comes first.
- Function composition means feeding the output of one function into another, written f(g(x)) — you always evaluate the inner function g(x) first, then use that result as the input to f.
- The order matters: f(g(x)) is generally not the same as g(f(x)), since evaluating them in the opposite order plugs values into different functions.
- Composition is common in describing chained processes, like converting units and then applying a formula, or applying multiple transformations to data in sequence.
How do I compute a composed function f(g(x))?
First substitute your value of x into g(x) and simplify to get a number. Then substitute that resulting number into f(x) in place of x, and simplify again.
What is f(g(3)) if f(x) = 2x + 1 and g(x) = x²?
First g(3) = 3² = 9, then f(9) = 2(9) + 1 = 19.