\(\left\{{}\begin{matrix}a^2\ge0\\a^4+1>0\end{matrix}\right.\) \(\Rightarrow f\left(a\right)\ge0\) \(\forall a\)
\(\Rightarrow f\left(a\right)_{min}=0\) khi \(a=0\)
\(f\left(a\right)=\frac{a^2}{a^4+1}\le\frac{a^2}{2a^2}=\frac{1}{2}\)
\(\Rightarrow f\left(a\right)_{max}=\frac{1}{2}\) khi \(a^2=1\)