Question 42
Determine all functions $f: \mathbb{R} \backslash\{0\} \rightarrow \mathbb{R}$ for which applies
$$
\frac{1}{x} f(-x)+f\left(\frac{1}{x}\right)=x \quad \forall x \in \mathbb{R} \backslash\{0\}
$$
$$
\frac{1}{x} f(-x)+f\left(\frac{1}{x}\right)=x \quad \forall x \in \mathbb{R} \backslash\{0\}
$$