Let f(x) = l x^2 + k, ; ; ; ; when ; ;x 0 - x^2 - k, ; ; when , ,… - Vidyadip

MCQ

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

A
$0$
B
$1$
C
$2$
D
$-2$

✓

Answer

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

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