Question

If $f\left(x\right)=\frac{1}{\sqrt{x^2+4}}$ and $g\left(x\right)=\sqrt{x}$ are two real functions, then the domain of $fog\left(x\right)$ is

$\left(a\right)[0,\infty )\left(b\right)R$
$\left(c\right)(-4,\infty )\left(d\right)[-4,\infty )$

Answer 1

$f\left(x\right)=\frac{1}{\sqrt{x^2+4}}$
$g\left(x\right)=\sqrt{x}$
$fog\left(x\right)=f\left(g\right(x\left)\right)=\frac{1}{\sqrt{(\sqrt{x}{)}^2+4}}=\frac{1}{\sqrt{x+4}}$
$\Rightarrow x+4>0$
Thus, the function $fog\left(x\right)$ is defined on $(-4,\infty )$.
Ans : $\left(c\right)$