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

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

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

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