A Tribute to an Ingenious Mind: Kishlaya Jaiswal

Calculus Level 5

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

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

(b) f(0)=2f(0)=2

If α\alpha is a Real Number and both β\beta and γ\gamma are positive integers

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

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

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