Let f : N -> N be a function such that f(m + n) = f(m) + f(n) for every m, n
N. If f(6) = 18, then f(2). f(3) is equal to :
Let f : N -> N be a function such that f(m + n) = f(m) + f(n) for every m, n N. If f(6) = 18, then f(2). f(3) is equal to :
Option 1 -
18
Option 2 -
36
Option 3 -
54
Option 4 -
6
Asked by Shiksha User
-
1 Answer
-
Correct Option - 3
Detailed Solution:f (m + n) = f (m) + f (n)
put m = n = 1, f (2) = f (1) + f (1)
again put m = 2, n = 1, f (3) = f (2) + f (1)
and put m = 3, n = 3, f (3 + 3) = f (3) + f (3), 2f (3) = f (6) = 18 Þ f (3) = 9
f (3) = 3f (1)
f (1) = 3, f (2) = 6
f (2).f (3) = 54
Taking an Exam? Selecting a College?
Get authentic answers from experts, students and alumni that you won't find anywhere else
Sign Up on ShikshaOn Shiksha, get access to
- 65k Colleges
- 1.2k Exams
- 682k Reviews
- 1800k Answers