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Range

Let S be the ...

Question

Let S be the set of all functions from the set A to the set A. If $n (A) = k$ then $n (S)$ is

k

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k^{k}

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2^{k} - 1

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2^{k}

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Solution

The correct option is C $k^{k}$
Given, $n (A) = k$

defining a function implies that every element in A is mapped to exactly one element in A

so, every element in A has k choices to make in the range set A.
likewise, there are k elements in A

$∴$ number of functions that can be defined = $k \times k \times k \times k \times$ ..... (k times)

i.e. $k^{k}$

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