Let A={1,2,3,5,8,9} . Then number of possible functions f : A → A such that f(m · n)=f(m) · f(n)

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1.Relation and Function

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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 $...............$.

A

$431$

B

$432$

C

$430$

D

$894$

(JEE MAIN-2023)

Solution

$f (1)=1 ; f (9)= f (3) \times f (3)$

i.e., $f(3)=1$ or $3$

Total function $=1 \times 6 \times 2 \times 6 \times 6 \times 1=432$

Standard 12

Mathematics

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