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  2. Question
  3. Mathematics
  4. Let A= 1,2,3,5,8,9 . Then the number of possible functions f: A arrow A such that f(m ⋅ n)=f(m) ⋅ f(n) for every m, n ∈ A with m ⋅ n ∈ A is equal to

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Q. Let $A=\{1,2,3,5,8,9\}$. Then the number of possible functions $f: A \rightarrow A$ 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______

JEE MainJEE Main 2023Relations and Functions

Solution:

$f(1)=1 ; f(9)=f(3) \times f(3)$
i.e., $f(3)=1$ or 3
Total function $=1 \times 6 \times 2 \times 6 \times 6 \times 1=432$