# A Tribute to an Ingenious Mind: Kishlaya Jaiswal

Calculus Level 5

Let $f(x)$ be a function with two properties:

(a) For any two real numbers $x$ and $y$, $f(x+y) = x + f(y)$ and

(b) $f(0)=2$

If $\alpha$ is a Real Number and both $\beta$ and $\gamma$ are positive integers

$\arcsin (f(100)) = \alpha - i\ln(\beta+\sqrt{\gamma})$

Evaluate $\lfloor \alpha \beta \gamma \rfloor$.

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