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

- 3
- 0
- 14.0625
- 15.9375

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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*

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

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