Functional Equations

Candidate checker

Test a guessed ff on many inputs and see the first failure.

For checking your work after you’ve tried it yourself.

Step 1:
Type the equation

Using f, like f(x+y) = f(x) + f(y).

Step 2:
Add your guesses

Up to three, like 2x or x^2.

Step 3:
Run the check

See which pass, and the first failure for the rest.
What it does.
Tests guessed functions in a functional equation at many inputs and shows, for each guess, whether it passes, or the first input where it fails with both sides worked out.
When it helps.
Checking a candidate you found before proving it works.
What it won’t do.
Passing is evidence, not proof that it works, and never proof that it's the only solution.
Example.
For f(x+y)=f(x)+f(y)f(x+y) = f(x) + f(y), f(x)=2xf(x) = 2x passes and f(x)=x2f(x) = x^2 fails at x=y=1x = y = 1.
A functional equation in f, with variables x, y, z
f(x)=f(x) =
f(x)=f(x) =
f(x)=f(x) =
Domain
Points per candidate

For example f(x+y) = f(x) + f(y). Each candidate is a formula in x.

Try

Checked with decimals at many points. Passing is evidence, not a proof that f works, and never a proof that it's the only answer.