Question 29
Let $f: \mathbb{R} \to \mathbb{R}$ be a strictly increasing function, and $f(x) \gt x$ for every $x$. Assume that
$$ f(x) + f^{-1}(x) = 2x $$
for all $x \in \mathbb{R}$. Show that $f(x) = x + f(0)$ for all $x \in \mathbb{R}$.
$$ f(x) + f^{-1}(x) = 2x $$
for all $x \in \mathbb{R}$. Show that $f(x) = x + f(0)$ for all $x \in \mathbb{R}$.