Find Possible valves of expression x2

$$\begin{gathered} Possible values of \frac{1}{x^2+2}= RANGE of \frac{1}{x^2+2} \\ So let \frac{1}{x^2+2}=y \\ =y{x}^2+2y=1 \\ \Rightarrow y{x}^2+2y-1=0 \\ D=b^2-4ac=0^{2}4\left(y\right)(2y-1) \\ =-4y(2y-1) \\ For x to be real D>0 \\ \Rightarrow -4y(2y-1)>0 \\ \Rightarrow 4y(2y-1)<0 \\ \Rightarrow y(2y-1)<0 \\ \Rightarrow Graph of above function is \\ \therefore y\in \left(0, \frac{1}{2}\right) \\ \mathbf{\therefore }\mathit{R}\mathit{a}\mathit{n}\mathit{g}\mathit{e}\mathbf{ }\mathit{o}\mathit{f}\mathbf{ }\frac{\mathbf{1}}{{\mathbf{x}}^{\mathbf{2}}\mathbf{+}\mathbf{2}}\mathit{i}\mathit{s}\mathbf{ }(0,\frac{1}{2}) \end{gathered}$$