1. ## Functions

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Why is the following assertion false? "If f(2)=2 and f(4)=4, then f(3)=3."
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this is that last problem on one of my homeworks. I think it is a trick question and that it is actually true...but i am not sure. please help, thanks.

2. Originally Posted by talhaguy
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Why is the following assertion false? "If f(2)=2 and f(4)=4, then f(3)=3."
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this is that last problem on one of my homeworks. I think it is a trick question and that it is actually true...but i am not sure. please help, thanks.
It is sometimes true.
Consider,
$\displaystyle f(x)=x$.

It is false when you consider
$\displaystyle f(x)=x+(x-2)(x-4)$

3. Hello, talhaguy!

Why is the following assertion false?
"If $\displaystyle f(2)=2$ and $\displaystyle f(4)=4$, then $\displaystyle f(3)=3.$"

All we know about the function are two points: $\displaystyle (2,2),\:(4,4)$

The graph could look like this:
Code:
      |
|                *
|             *     *(4,4)
|           *       :
|          *        :
|                   :
|    (2,2)*         :
|         :         :
|         :         :
|         :         :
-+---------+----+----+------
|         2    3    4

That is, $\displaystyle f(3)$ could be anywhere on the line $\displaystyle x = 3.$

4. thankyou so much guys, i really appreciate it.