examday

/TMUA

For a real number $a$, define

Call $a$ admissible if both of the following hold:

• $F_a$ is not one-to-one on the positive real numbers;

• for every pair of distinct positive reals $x,y$ with $F_a(x)=F_a(y)$, at least one of the inequalities

  $\displaystyle |x-y|<4,\qquad \frac{\max\{x,y\}}{\min\{x,y\}}<5$

  holds.

Which one of the following is exactly the set of admissible values of $a$?