Problems aren't periodic but random

Calculus Level pending

Define a function periodic \(f\left( x \right)\) with period 'a' , takes real values and satisfies \(\frac { \sqrt { 3 } }{ \sqrt { 2 } } f\left( x+\frac { 11 }{ 6 } \right) = f\left( x \right) +f\left( x+\frac { 11 }{ 3 } \right) \).

Another periodic function \(g\left(x\right)\) with period 'b' ,takes real values and satisfies \(2g\left( x-2 \right) +2g\left( x+2 \right) =\sqrt { 6 } g\left( x \right) \). Find:\(a\times b\).

This problem is original. Try this also.
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