Question

Let $f\left(x\right)=\frac{\sqrt{x^2+kx+1}}{x^2-k}$ is continuous for every $x\in R$ then set of values of $k$ is

• A. $(-\infty ,-2]$
• B. $[-2,0)$
• C. $R-(-2,2)$
• D. $(-2,2)$

Answer 1

The correct option is B $[-2,0)$

$x^2-k\ne 0\forall x\in R$
$\Rightarrow k<0$ $...\left(1\right)$
$x^2+kx+1\ge 0\forall x\in R$
$\Rightarrow k^2-4\le 0\Rightarrow -2\le k\le 2$ $...\left(2\right)$
$\therefore$ From $\left(1\right)$ and $\left(2\right)$
$k\in [-2,0)$