Thread: continuous function

how do you prove this:

let f: real numbers -> real numbers be continuous and bounded and define g as g(x) = sup {f(x) : y< x}. prove that g is continuous.

this is what i did:

i wrote the def of continuous function for f, assuming that f is cont at the pt c and then i got stuck..

The function g is monotone--what kinds of discontinuities can a monotone function have?