Question 105
a) Show that the set $M$ is non-empty.
b) Find all numbers $a \in \mathbb{R}$ such that $f(a)=0$ holds for at least one function $f \in M$.
c) Find all numbers $a \in \mathbb{R}$ such that $f(a)=0$ holds for all functions $f \in M$.
where $M=\{f: \mathbb{R} \rightarrow \mathbb{R} \mid f(2 f(x)+x)+f(x)=4 x-4\}$.
b) Find all numbers $a \in \mathbb{R}$ such that $f(a)=0$ holds for at least one function $f \in M$.
c) Find all numbers $a \in \mathbb{R}$ such that $f(a)=0$ holds for all functions $f \in M$.
where $M=\{f: \mathbb{R} \rightarrow \mathbb{R} \mid f(2 f(x)+x)+f(x)=4 x-4\}$.