# If f(x+y) = f(x) f(y) and f(5) = 4 -Quantitative Aptitude – Equation

## CAT 2020 – Slot -3- If f(x+y) = f(x) f(y) and f(5) = 4

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

##### 1. 32. 03. 14.06254. 15.9375

9. 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) = 1/16 = 0.0625

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

Note: You need not know or calculate the exact value of 1/16

Whatever 1/16 is, we know that it is less than 1/2

So, the valuve 16 – 1/16, will be greater than 16 – 1/2 or 15.5

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