please see the following question

7 A function f : R" > R is coercive if lim f (x) = 00. \"mu->00 Explicitly, this condition means that for any M > 0 there is an R > 0 such that \"x\" 2 R implies f (:13) 2 M. Prove that if f : R\" > R is lower semicontinuous and coercive, then f is bounded from below and attains its inmum