CAT 2017 Question Paper | Quants Slot 2

CAT Questions

CAT Previous Year Papers give you a flavour of the CAT Exam and type of questions asked in the CAT Question Paper. Your online CAT preparation is incomplete without going through the actual questions asked in the CAT Examover the years. Don't fall short in covering this important element of CAT preparation and start with this question on Functions taken from CAT 2017 Question Paper.
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Question 31 : If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is [TITA]

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Video Explanation

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Explanatory Answer

Method of solving this CAT Question from Functions

Given that f(ab) = f(a) × f(b) for all possible integers a and b.
We have to find the largest possible value of f(1). We know that,
f(ab) = f(a) × f(b)
⟹ f(a × 1) = f(a) × f(1)
⟹ [f(a) × f(1)] – f(a) = 0
⟹ f(a)[f(1) – 1] = 0
There are two possibilities here, either f(a) = 0 or f(1) – 1 = 0.
If f(a) = 0, then it is a constant function. Hence, f(1) = 0.
But, if f(1) – 1 = 0, f(1) = 1.
Hence, f(1) = 0 or f(1) = 1.
Out of these, f(1) = 1 is the largest possible value.

The question is "If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is [TITA]"

Hence, the answer is 1