If atomic electron is in $f$-state, what values of the total angular momentum are allowed?

If $l=3$ and $s=1/2$ then the values of total angular momentum can take lie within the following range:

$$|l-s|leq Jleq l+s$$

With $J$ incrementing by 1 between these two bounds.

$$therefore 5/2leq Jleq7/2$$

$J$ can take values $5/2$ and $7/2$

If you have a single electron system then your z component of total angular momentum can take on values -5/2,-3/2,-1/2, 1/2, 3/2, 5/2 for J=5/2 and -7/2,-5/2,-3/2,-1/2, 1/2, 3/2, 5/2, 7/2 for J=7/2. Overall you have 14 possible states your electron can be in.