Set f a lower semicontinuous real function. If the set of points such that f(x)=c is dense. Then c is an upper bound for f(x) for all x?

Set $f$ lower semicontinuous real function.Supose the set of x such that $f(x)=c$ is dense.

Then $f(x)<= c$ for all $x$ or $f(x) >= c$ for all $x$ ?

Im inclined to belive that its the second option. By the definition of lower semicontinuous.