I have been trying to solve this challenging question which is entitled bonus on the document posted, does anyone have an idea of how to go about solving it.
I have been trying to solve this challenging question which is entitled bonus on the document posted, does anyone have an idea of how to go about solving it.
Thx in advance!
Let $\displaystyle f:I\mapsto I$ continually ([tex]I=[0,1]). Let $\displaystyle g(x)=f(x)-x$. More obvious now. Consider the function at the endpoints.
I have been trying to solve this challenging question which is entitled bonus on the document posted, does anyone have an idea of how to go about solving it.
Thx in advance!
lol...if you promise to "thank me" ill do it first thing tomorrow morning. looks str8forward...but i need sleep and ive been getting ripped off with posters not thanking me today
I am not quite sure what you mean by what you wrote. Can you please explain in more depth.
thanks.
Think about it this way, $\displaystyle h(x)=f(x)-x$ h(0)=f(0)0\geqlsant 0-0=0[/tex] if it's zero we're done. Otherwise it's greater than zero. Similarly $\displaystyle h(1)=f(1)-1\leqslant 1-1=0$. If it's equal zero zero we're done. Otherwise it's less than zero.
lol...if you promise to "thank me" ill do it first thing tomorrow morning. looks str8forward...but i need sleep and ive been getting ripped off with posters not thanking me today
well its stating that a continuous function will take on values within a specific domain, in other words between f(a) and f(b)
Ok, so we know that $\displaystyle h(0)\geqslant 0$ and [math\h(1)\leqslant 0[/tex] if either are zero we're done, so assume that neither are. Then $\displaystyle h(0)>0,h(1)<0$