Consider the function $f(x)= \begin{cases}\frac{\tan k x}{x}, & x \lt 0 \\ 3 x+2 k^2, & x \geq 0\end{cases}$ What is the non-zero value of $k$ for which the function is continuous at $x=0$ ?

• A

  $\frac{1}{4}$
• Correct answer
  B

  $\frac{1}{2}$
• C

  1
• D

  2

Hence, the correct answer is option: 'B'.