If the function \(f(x)=\left{\begin{matrix}\frac{1}{x}{\log }_{e}\left(\frac{1+\frac{x}{a}}{1-\frac{x}{b}}\right), & ,x …

If the function

\(f(x)=\left{\begin{matrix}\frac{1}{x}{\log }_{e}\left(\frac{1+\frac{x}{a}}{1-\frac{x}{b}}\right), & ,x<0 \\ k & ,x=0 \\ \frac{{\cos }^{2}x-{\sin }^{2}x-1}{\sqrt{{x}^{2}+1}-1}, & x>0\end{matrix}\right.\)

is

continuous at \( x=0 \), then \( \frac{1}{a}+\frac{1}{b}+\frac{4}{k} \) is equal to:

[JEE Main 2021, 31 Aug (Shift 1)]