Let S - 1- 2- 3- 4- 5- 6- 7 - Then the number of possible functions f - S - S such that fm- n-fm- fn for every m-n- S and m- n- S is equal to

Given f(m · nbsp; n) = f(m)· f(n) Clearly, f(1) = 1 nbsp; nbsp; Total number of ways = 7^3 + 3· 7^2 = 490 ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Fundamental Principle of Counting

Let S = 1, 2,...

Question

Let $S = {1, 2, 3, 4, 5, 6, 7}$ . Then the number of possible functions $f : S \to S$ such that $f (m \cdot n) = f (m) \cdot f (n)$ for every $m, n \in S$ and $m \cdot n \in S$ is equal to

Open in App

Solution

Given $f (m \cdot n) = f (m) \cdot f (n)$
Clearly, $f (1) = 1$

Total number of ways $= 7^{3} + 3 \cdot 7^{2} = 490$

Suggest Corrections

Similar questions

Q. Let

S

be the set of all triangles and

R^{+}

be the set of positive real numbers. Then the function

f : S \to R^{+}, f (△) = Area of △, where △ \in S

, is

Let $ln x$ denote the logarithm of $x$ with respect to the base $e$ . Let $S \subset R$ be the set of all points where the function $ln (x^{2} - 1)$ is well-defined. Then the number of functions $f : S \to R$ that are differentiable, satisfy $f^{'} (x) = ln (x^{2} - 1)$ for all $x \in S$ and $f (2) = 0$ , is