# Thread: Bonus Question involving Continuity?

1. ## Bonus Question involving Continuity?

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.

2. Originally Posted by Solid8Snake
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.

Let $f:I\mapsto I$ continually ($$I=[0,1]). Let $g(x)=f(x)-x$. More obvious now. Consider the function at the endpoints. 3. I am not quite sure what you mean by what you wrote. Can you please explain in more depth. thanks. 4. Originally Posted by Solid8Snake I have been trying to solve this challenging question which is entitled bonus on the document posted, does anyone have an idea of how to go about solving it. Thx in advance! lol...if you promise to "thank me" ill do it first thing tomorrow morning. looks str8forward...but i need sleep and ive been getting ripped off with posters not thanking me today 5. Originally Posted by Solid8Snake I am not quite sure what you mean by what you wrote. Can you please explain in more depth. thanks. Think about it this way, $h(x)=f(x)-x$ h(0)=f(0)0\geqlsant 0-0=0$$ if it's zero we're done. Otherwise it's greater than zero. Similarly $h(1)=f(1)-1\leqslant 1-1=0$. If it's equal zero zero we're done. Otherwise it's less than zero.

6. Originally Posted by vince
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
What a stupid thing to say.

7. I am very confused, I read what you stated, but like I'm not sure how to apply it since we haven't really used the theorem in depth.

8. Originally Posted by Solid8Snake
I am very confused, I read what you stated, but like I'm not sure how to apply it since we haven't really used the theorem in depth.
What does the IVT say?

9. whether there is a root within a given interval

10. Originally Posted by Solid8Snake
whether there is a root within a given interval
Not really. Look it up, look at what I said and get back to me.

11. well its stating that a continuous function will take on values within a specific domain, in other words between f(a) and f(b)

12. so in other words would this be sort of what we are getting at
0<c<1?

13. Originally Posted by Solid8Snake
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 $h(0)\geqslant 0$ and [math\h(1)\leqslant 0[/tex] if either are zero we're done, so assume that neither are. Then $h(0)>0,h(1)<0$

14. I think I get it now.

Thanks for the help!

15. Originally Posted by Drexel28
What a stupid thing to say.
easy for you to say

... most of the problems are fun for me, so in some sense i should thank them ...lol...cornfest.

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