examday

/TMUA

The functions $f$ and $g$ are defined for all real numbers, take real values, and satisfy

for every real $x$.

Consider the following statements.

1. For all real $u$ and $v$, if $g(u)=g(v)$, then $u=v$.
2. For every real $y$, there is a real $t$ such that $f(t)=y$.
3. For every real $x$, $g(f(x))=x$.

Which statements must be true?