# CAT 2020 Quant Question [Slot 3] with Solution 08

Question

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

1. 0
2. 15.9375
3. 3
4. 14.0625
Option: 2
Solution:

Given $f(x + y) = f(x)f(y)$

$\Rightarrow f(x) = {a^x}$( where $a$ is a constant ) Given, $f(5) = 4 \Rightarrow {a^5} = 4 \Rightarrow a = {2^{2/5}}$

$f(10) - f( - 10) = {a^{10}} - {a^{ - 10}} = {\left( {{2^{\frac{2}{5}}}} \right)^{10}} - {\left( {{2^{\frac{2}{5}}}} \right)^{ - 10}}$

$= {2^4} - {2^{ - 4}} = 16 - \frac{1}{{16}} = 15.9375$

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