CAT 2020 Slot 3 QA Question & Solution
AlgebraMedium
Question
If $f(x+y)=f(x)f(y)$ and $f(5)=4$, then $f(10)-f(-10)$ is equal to
Options
14.0625
0
15.9375
3
Solution
The given function is equivalent to f(x) = $a^x$
Given, f(5) = 4
=> $a^5=4=>\ a=4^{\frac{1}{5}}$
=> f(x) = $4^{\frac{x}{5}}$
f(10) - f(-10) = 16 - 1/16 = 15.9375