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Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) < f="" (2),="" and="" f="" (24)="54," then="" f="" (18)="" />
Correct answer is '12'. Can you explain this answer?
Verified Answer
Let f be a function such that f (mn) = f (m) f (n) for every positive...
Given, f(mn) = f(m)f(n)
when m= n= 1, f(1) = f(1)*f(1) ==> f(1) = 1
when m=1, n= 2, f(2) = f(1)*f(2) ==> f(1) = 1
when m=n= 2, f(4) = f(2)* f(2) ==> f(4) = [f(2)]2
Similarly f(8) = f(4)*f(2) =[f(2)]3
f(24) = 54
[f(2)]3 * [f(3)] = 33 * 2
On comparing LHS and RHS, we get
f(2) = 3 and f(3) = 2
Now we have to find the value of f(18)
f(18)=[f(2)]*[f(3)]2
=3*4=12
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Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) Correct answer is '12'. Can you explain this answer?
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Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) Correct answer is '12'. Can you explain this answer? for CAT 2024 is part of CAT preparation. The Question and answers have been prepared according to the CAT exam syllabus. Information about Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) Correct answer is '12'. Can you explain this answer? covers all topics & solutions for CAT 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for Let f be a function such that f (mn) = f (m) f (n) for every positive integers m and n. If f (1), f (2) and f (3) are positive integers, f (1) Correct answer is '12'. Can you explain this answer?.
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