Let \(f\) and \(g\) be functions satisfying \(f(x+y)=\)\(f(x)f(y),\text{ }f(1)=7\) and \(g(x+y)=g(xy)\), \(g(1)=1,\) for…

Let \(f\) and \(g\) be functions satisfying \(f(x+y)=\)\(f(x)f(y),\text{ }f(1)=7\) and \(g(x+y)=g(xy)\), \(g(1)=1,\) for all \(x,\text{  }y\in N.\) If \(\sum _{x=1}^{n}\left(\frac{f(x)}{g(x)}\right)=19607,\) then \(n\) is equal to:

[JEE Main 2026, 22 Jan (Shift 2)]