Thread: Bonus Question involving Continuity?

I thought about the question overnight, but still didn't know how to do it. Someone please help me. When I look at part of the thing you wrote it looks like some type of foreign code, which is why i'm not quite sure what you are trying to say.

you wrpte and I quote "[math\h(1)\leqslant 0[/tex]" what does that mean?

Ok h(x) = f(x) - x

h(0) = f(0) >= 0 since the range is [0,1] if h(0) = 0 then f(0) = 0 done

suppose then h(0) > 0

h(1)= f(1) - 1 < = 0 again since the range is [0,1]

If h(1) = 0 f(1) = 1 done
if not h(1) > 0

since h(1) >0 and h (0) < 0 then there is a c st h(c) = 0

h(c) = f(c) - c = 0 i.e f(c) = c

Thanks a million calculus its so much more clearer now. Sorry If I was being a bit of a pain