Distribution function related with the limit from left show that the distribution fun $F$ of random variable $f$ takes only values $0$ and $1$ iff there exists areal number $c$ such that $P(f=c)=1$ ??
I begin solve the ex and i prove $F$ takes two value $0$ and $1$ (one side ) 
another side I had  problem 
suppose $F$ takes two values $0$ and $1$ ,
 we must found $c$ satisfies $P(f=c)=1$ 
but I know $P(f=c)=P(f\leq c)-P(f<c)$ 
and I know $P(f<c)=\lim F(x)$ as $x$ approached to $c$ from left 

Hint:
Define $c:=\inf\{x\in \mathbb R\mid F(x)=1\}$
Then, since $F$ is continuous from the right, we have $F(c)=1$.
What can be said about $F(x)$ if $x<c$?
What does that say about $P(f=c)$?
