Question 32.
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) equals
A
B
C
D
Question Explanation
Text Explanation
Video Explanation
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) =
Similarly f(8) = f(4)*f(2) =
f(24) = 54
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)] *
= 3*4=12
No video explanation yet — we're on it and uploading soon!
