3. The maximum value $M(a)$ of the function $f(x)=\left|x^{2}-a\right|$ on the interval $[-1,1]$ has its minimum value as

保留源文本的换行和格式，翻译结果如下：

3. The maximum value $M(a)$ of the function $f(x)=\left|x^{2}-a\right|$ on the interval $[-1,1]$ has its minimum value as
3. $\frac{1}{2}$ Detailed Explanation: $M(a)=\left\{\begin{array}{l}1-a,\left(a \leqslant \frac{1}{2}\right) \\ a,\left(a \geqslant \frac{1}{2}\right)\end{array}\right.$, when $a=\frac{1}{2}, M(a)_{\min }=\frac{1}{2}$.