Question 97
Find all functions $f: \mathbb{R} \rightarrow \mathbb{R}$ satisfying the following conditions
(a) $f(1)=1$
(b) $\forall (x, y) \in \mathbb{R}^2$, $f(x+y)=f(x)+f(y)$
(c) $\forall x \in \mathbb{R} \setminus \{0\}$, $f\left(\frac{1}{x}\right)=\frac{f(x)}{x^2}$.
(a) $f(1)=1$
(b) $\forall (x, y) \in \mathbb{R}^2$, $f(x+y)=f(x)+f(y)$
(c) $\forall x \in \mathbb{R} \setminus \{0\}$, $f\left(\frac{1}{x}\right)=\frac{f(x)}{x^2}$.