QJEEM23Maafb2: JEE Main 2023 Mathematics - Class 11 JEEM23Maafb2 Solution: Let . Then the number of possible functions such that for every …

Question

Verified Solution • 2025–26 Session moderate

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 ___________.

Accepted Answer

$f (1. n) = f (1) . f (n) \Rightarrow f (1) = 1$ .

$f (3.3) = (f (3))^{2}$

Hence, the possibilities for $(t (3), (9))$ are $(1, 1)$ and $(3, 9)$ .

Other three i.e. $f (2), f (5), f (8)$

Can be chosen in 6 $^{3}$ ways.

Hence, total number of functions

$6^{3} \times 2 = 432$

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