Composite Function Calculator
Evaluate f(g(x)) for two linear functions.
Enter your values
Enter the f slope m1 you are working with.
Enter the f intercept b1 you are working with.
Enter the g slope m2 you are working with.
Enter the g intercept b2 you are working with.
Enter the x value you are working with.
Results update instantly as you type — no submit needed. Your values are remembered on this device, and the shareable link reopens the calculator with exactly these numbers.
- 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.
f(g(x)) = m1(m2x+b2)+b1
At a glance
| What it does | Evaluate f(g(x)) for two linear functions. |
|---|---|
| Category | Math |
| Inputs needed | f slope m1, f intercept b1, g slope m2, g intercept b2, x value |
| Main output | f(g(x)) |
| Formula | f(g(x)) = m1(m2x+b2)+b1 |
| Cost | Free — no sign-up, no download |
How to use the Composite Function Calculator
- 1Enter the slope and intercept for f and for g.
- 2Enter the x value to evaluate.
- 3Read both compositions f(g(x)) and g(f(x)) — they are usually different.
Inputs explained
- f slope m1
- Enter the f slope m1 you are working with.
- f intercept b1
- Enter the f intercept b1 you are working with.
- g slope m2
- Enter the g slope m2 you are working with.
- g intercept b2
- Enter the g intercept b2 you are working with.
- x value
- Enter the x value you are working with.
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
Results
- f(g(x))21
- g(x)10
- g(f(x))25
- f(x)9
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.
What do I need to enter into the Composite Function Calculator?
Just 5 values: f slope m1, f intercept b1, g slope m2, g intercept b2, x value. Every field starts with a realistic example, so you can change one number at a time and watch the result update instantly.
How does the Composite Function Calculator work out the answer?
f(g(x)) plugs g(x) into f, so f(g(x)) = m1*(m2*x+b2)+b1. It applies the formula f(g(x)) = m1(m2x+b2)+b1 and shows the working so you can check each step by hand.
Is the Composite Function Calculator free, and do I need an account?
It is completely free with no sign-up, no download and no usage limit. Everything is calculated in your browser, so the numbers you type never leave your device.
Results are estimates for general information. For medical, legal, structural or financial decisions, confirm with a qualified professional.