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)

English

Gujarati

Hindi

1.Relation and Function

medium

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

Share

Similar Questions

If $f\left( x \right) = {\log _e}\,\left( {\frac{{1 – x}}{{1 + x}}} \right)$, $\left| x \right| < 1$, then $f\left( {\frac{{2x}}{{1 + {x^2}}}} \right)$ is equal to

hard

(JEE MAIN-2019)

The range of values of the function $f\left( x \right) = \frac{1}{{2 – 3\sin x}}$ is

normal

If $f$ is an even function defined on the interval $(-5, 5)$, then four real values of $x$ satisfying the equation $f(x) = f\left( {\frac{{x + 1}}{{x + 2}}} \right)$ are

normal

If $f(x)$ is a function satisfying $f(x + y) = f(x)f(y)$ for all $x,\;y \in N$ such that $f(1) = 3$ and $\sum\limits_{x = 1}^n {f(x) = 120} $. Then the value of $n$ is

hard

(IIT-1992)

If $0 < x < \frac{\pi }{2},$ then

normal