2.2. Find all values of $a$ for which the quadratic function $f(x)=a x^{2}-4 a x+1$ takes values, the modulus of which does not exceed 3, at all points of the interval $[0 ; 4]$. In your answer, specify the total length of the intervals to which the found values of $a$ belong.
Answer: 1.5 (the set of values for $a$: $\left[-\frac{1}{2} ; 0\right) \cup(0 ; 1]$ ).