Question

Let $f\left(x\right)=\{\begin{array}{ccc}{x}^2+k,& when& x\ge 0\\ -x^2-k,& when& x<0\end{array}$. If the function f (x) be continuous at x = 0, then k =

• A. 1
• B. 2
• C. -2

Answer 1

Here ${lim}_{x\to 0}f\left(x\right)=k,{lim}_{x\to 0-}f\left(x\right)=-k$ and f(0)=k
But f(x)is continuous at x = 0,therefore k must be zero.