Let A = {1, 2, 3, 4, 5}. How many functions f from A to A satisfy f(f(x)) = f(x) for every x in A? (Such a function does nothing more when it is applied a second time.)

MathematicsAdvancedHigh School (11–12)Functions and Calculus › Counting Functions JEE Advanced

Let $A = \{1, 2, 3, 4, 5\}$ . How many functions $f$ from $A$ to $A$ satisfy $f(f(x)) = f(x)$ for every $x$ in $A$ ? (Such a function does nothing more when it is applied a second time.)

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← A polynomial f with real coefficients satisfies f(x) f(y) = f(x) + f(y) + f(xy) - 2 for all real x and y, and f(2) = 5. Which of the following statements are correct?A relation on A = {1, 2, 3, 4} is any subset of A × A, the empty relation included. How many relations on A are symmetric and transitive but not reflexive? →

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