Question

The total number of function from $A$ to itself is $256$, then $n\left(A\right)=$

• A. $2$
• B. $3$
• C. $4$
• D. $5$

Answer 1

Answer: (C)

$4$

Let $n\left(A\right)=x$
each element of x in domain can be mapped onto
each element of x in the range.
$\Rightarrow$ Total number of functions is $x\times x\times ...\times x$
$\Rightarrow x^x=256$
$\Rightarrow x=4$