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Calculation Machine

Composite Function Calculator

Evaluate f(g(x)) for two linear functions.

Reviewed by the Calculation Machine team · How we check our maths

Your values

ⓘ Live results

Results
f(g(x))
21
g(x)
10
g(f(x))
25
f(x)
9

Quick answer

f(g(x)) plugs g(x) into f, so f(g(x)) = m1*(m2*x+b2)+b1.

The formula

f(g(x)) = m1(m2x+b2)+b1

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • f slope m12
  • f intercept b11
  • g slope m23
  • g intercept b2-2
  • x value4

Result

  • f(g(x))21
  • g(x)10
  • g(f(x))25
  • f(x)9

How to use the Composite Function Calculator

  1. 1Enter the slope and intercept for f and for g.
  2. 2Enter the x value to evaluate.
  3. 3Read both compositions f(g(x)) and g(f(x)) — they are usually different.

Frequently asked questions

Is f(g(x)) the same as g(f(x))?

Not usually — function composition is not commutative in general.

Can this handle non-linear functions?

This tool models linear functions; substitute manually for higher-degree functions.

About this calculator