Question 45
Given a function $f(x) = x^2 + bx + c$, where $b, c \in \mathbb{R}$ and $b \ge 0$. Is it possible to represent the segment $[0, 1]$ as the union $A \cup B$ of two disjoint sets $A$ and $B$ such that $f(A) = B$?
Recall that $f(A)$ denotes the image of the set $A$, that is, $f(A) = \{f(a) \mid a \in A\}$.
Recall that $f(A)$ denotes the image of the set $A$, that is, $f(A) = \{f(a) \mid a \in A\}$.