Let f: R → R be a function given by f(x)= {(1- cos 2 x)/x^2, x<0; α, x=0, (β √(1- cos x))/x, x>0} where α, β ∈ R. If f is continuous at x=0, then…

Let $\displaystyle f: \mathbf{R} \rightarrow \mathbf{R}$ be a function given by $$f(x)=\left\{\begin{array}{cc} \frac{1-\cos 2 x}{x^2}, & x<0 \\ \alpha, & x=0, \\ \frac{\beta \sqrt{1-\cos x}}{x}, & x>0 \end{array}\right. $$ where $\displaystyle \alpha, \beta \in \mathbf{R}$. If $\displaystyle f$ is continuous at $\displaystyle x=0$, then $\displaystyle \alpha^2+\beta^2$ is equal to: