CAT 2020 Question Paper | Quants Slot 3

CAT Questions

This is an Unconventional Question. It is about a function which is a multiplication of two other functions. Functions is a simple topic which involves a lot of basic ideas. Make sure you practice a lot of questions in CAT Functions Algebra to push your CAT preparation in the right direction. Functions as an idea is a fabulous idea if one can wrap their head around it the right way, and it has been one of the staple ideas tested by the CAT exam historically.

Question 9 : If f(x+y) = f(x)f(y) and f(5) = 4, then f(10) - f(-10) is equal to

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Video Explanation

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Explanatory Answer

We are told that f(x+y) = f(x) × f(y)
f(x) = f(x + 0) = f(x) × f(0)
f(x) = f(x) × f(0)
Assuming that f(x) is non-zero;
This implies: f(0) = 1

f(5) = 4 (Given)
f(10) = f(5+5) = f(5) × f(5) = 4 × 4 = 16
f(10) = 16

we know that f(0) = 1
f(0) = f(10 - 10) = f(10 + (-10)) = f(10) × f(-10) = 1
16 × f(-10) = 1
f(-10) = \\frac{1}{16}) = 0.0625

f(10) - f(-10) = 16 - 0.0625 = 15.9375.

Note: You need not know or calculate the exact value of \\frac{1}{16})
Whatever \\frac{1}{16}) is, we know that it is less than \\frac{1}{2})
So, the valuve 16 - \\frac{1}{16}), will be greater than 16 - \\frac{1}{2}) or 15.5

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The question is "If f(x+y) = f(x)f(y) and f(5) = 4, then f(10) - f(-10) is equal to"

Hence, the answer is, "15.9375"