Let $f(x)=\left\{\begin{array}{1 1}\big[\tan(\large\frac{\pi}{4}\normalsize +x)\big]^{\large\frac{1}{x}}&x\neq 0\\k&x=0\end{array}\right.$.For what value of k,$f(x)$ is continuous at $x=0$

Question

$(a)\;e\qquad(b)\;0\qquad(c)\;1\qquad(d)\;e^2$