Let f: R -> R be defined by f(t)=t^2. Let U be any non empty open subset of R. Then which of the following options is correct?

a) f(U) is open

b) f^(-1) (U) is open

c)f(U) is closed

d) f^(-1)(U) is closed.

Hey:)

f(t) is a continuous function from R -> R. This implies for any open subset U in R f^(-1) (U) is open.

So i think b) is correct. Am I right? Or is f(U) open?