Idempotence of a Function

Number Theory Level 2

How many of the following functions are idempotent?

$\lfloor x \rfloor$
$|x|$
$x^2$
$\lceil x \rceil$
$\sqrt{x}$
$f(f(x))=f(x)$

6 4 None of These 5 All of Them 3

1 solution

Alex Delhumeau
May 31, 2015

From the given definition, an idempotent function is one that can be applied any number of times without changing the initial output.

The floor, ceiling, and absolute value all functions fit this definition, as does $f(x) = f(f(x))$ . $\Rightarrow \boxed{4}$ of the given functions are idempotent.

Idempotence of a Function

1 solution

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