Analysis proof continuous from left PLEASE HELP :)

I've been struggling on this one for hours so if someone could help me I would really really appreciate it!

Let f be a bounded function on [a,b]. Show that the function defined by m(x) = inf{f(w):w in [a,x)} is continuous from the left on (a,b).

I'm really looking forward to seeing your thoughts on this one! Thank you so much! :)

Re: Analysis proof continuous from left PLEASE HELP :)

Re: Analysis proof continuous from left PLEASE HELP :)

Well I was trying to use the definition: f is continuous from the left at x0 if f(x0)=limx->x0- f(x). But I'm not really sure what to do from your last step to get there. Can you lead me in the right direction please? :)

Re: Analysis proof continuous from left PLEASE HELP :)