Functions Question 16
Question 16 - 30 January - Shift 2
Let $A={1,2,3,5,8,9}$. Then the number of possible functions $f: A \to A$ such that $f(m \cdot n)=f(m) \cdot f(n)$ for every $m, n \in A$ with $m \cdot n \in A$ is equal to ________
Show Answer
Answer: 432
Solution:
Formula: Number of possible functions, Domain , Range
$f(1)=1 ; f(9)=f(3) \times f(3)$
i.e., $f(3)=1$ or 3
Total function $=1 \times 6 \times 2 \times 6 \times 6 \times 1=432$
