Question

Determine the value of the constant $k$ so that the function $f\left(x\right)=\{\begin{array}{c}\frac{kx}{\left|x\right|},ifx<0\\ 3,ifx\ge 0\end{array}$ is continuous at $x=0$

Answer 1

$f\left(x\right)=\{\begin{array}{ccc}\frac{kx}{|x|}& if& x<0\\ 3& if& x\ge 0\end{array}$

At $x=0^{-}$ $f\left(x\right)=\frac{kx}{-x}=-k$

At $x=0^{+}$ $f\left(x\right)=3$

$-k=3$

$k=-3$.