finite compliment and discrete topology question

Let the topological space X be $\displaystyle \Re$ with the finite complement topology, and let the topological space Y be $\displaystyle \Re$ with the discrete topology. Define a function

*f*: X---> Y by *f(x)* = $\displaystyle \Re$ - {x}. So, for example, If

U = $\displaystyle \Re$ - *C*, where *C* = {$\displaystyle {x_1,......,x_n}$}, then *f*(U) = *C*

(a) Is *f* continuous?Why or why not?

(b) What is $\displaystyle f^-1$?Is it continuous or not?

(c) Is *f* a homeomorphism? Why or why not?

Please help me out