What property does a function have if applying it twice yields the same result as applying it once?

• A. It is non-idempotent
• B. It is idempotent
• C. It is invertible
• D. It is monotonic

Answer: (B)

Idempotence is the property where applying a function twice yields the same result as applying it once. In other words, f(f(x)) = f(x) for every input x. This happens because after the first application, the output is already in a state that the function leaves unchanged if applied again—think of projecting onto a fixed set: once you’re projected, re-projecting doesn’t move you.

This is why that option fits best: after the first pass, further applications do not change the value, which is exactly what idempotence describes. For contrast, an invertible function isn’t defined by stability under a second application, and monotonicity deals with preserving order, not with repeated applications. A non-idempotent function would produce a different result when applied again.