a) The real number $a$ and the continuous function $f : [a, \infty) \rightarrow [a, \infty)$ are such that $|f(x)-f(y)| < |x–y|$ for every two different $x, y \in [a, \infty)$. Is it always true that the equation $f(x)=x$ has only one solution in the interval $[a, \infty)$? b) The real numbers $a$ and $b$ and the continuous function $f : [a, b] \rightarrow [a, b]$ are such that $|f(x)-f(y)| < |x–y|$, for every two different $x, y \in [a, b]$. Is it always true that the equation $f(x)=x$ has only one solution in the interval $[a, b]$?