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

A
k
B
kk
C
2k1
D
2k

Solution

## The correct option is C $$\displaystyle k^k$$Given, $$n(A) =k$$defining a function implies that every element in A is mapped to exactly one element in Aso, every element in A has k choices to make in the range set A.likewise, there are k elements in A$$\therefore$$ number of functions that can be defined =$$k\times k\times k\times k\times$$ ..... (k times)i.e. $${ k }^{ k }$$Mathematics

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