How many one-one functions f from {1, 2, 3} to {1, 2, 3, 4, 5} satisfy f(1) ≠ 1, f(2) ≠ 2 and f(3) ≠ 3? In other words, no element of the first set is sent to the number equal to itself.

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

How many one-one functions $f$ from $\{1, 2, 3\}$ to $\{1, 2, 3, 4, 5\}$ satisfy $f(1) \ne 1$ , $f(2) \ne 2$ and $f(3) \ne 3$ ? In other words, no element of the first set is sent to the number equal to itself.

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← Four relations are defined on the set ℤ of all integers, by saying when a is related to b. Which one of them is an equivalence relation, that is, reflexive, symmetric and transitive?The function f(x) = x² - 2x, taken on the domain [1, ∞), is one-one and maps onto [-1, ∞), so it has an inverse f⁻¹. For which real numbers x is f(x) = f⁻¹(x)? Both sides must be defined. →

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