Explanation
We have,
{{x}^{2}}+k\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,when,\,x\ge 0\,
-{{x}^{2}}-k\,\,\,\,\,\,\,\,\,\,\,\,\,when,x\le 0
Given that,
L.H.L=R.H.L=f\left( x \right)
At point x=0
{{x}^{2}}+k=-{{x}^{2}}-k=0
\Rightarrow {{x}^{2}}+k=0
\Rightarrow k=-{{x}^{2}}
\Rightarrow k=0
Hence, this is the answer.
Please disable the adBlock and continue. Thank you.