Question

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

• A. $0$
• B. $1$
• C. $2$
• D. $-2$

Answer 1

Answer: (A)

$0$

We have,

$x^2+kwhen,x\ge 0$

$-x^2-kwhen,x\le 0$

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.