# Functions

• January 9th 2007, 04:15 PM
talhaguy
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.
• January 9th 2007, 04:22 PM
ThePerfectHacker
Quote:

Originally Posted by talhaguy
___________________
Why is the following assertion false? "If f(2)=2 and f(4)=4, then f(3)=3."
___________________

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,
$f(x)=x$.

It is false when you consider
$f(x)=x+(x-2)(x-4)$
• January 9th 2007, 09:49 PM
Soroban
Hello, talhaguy!

Quote:

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

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

The graph could look like this:
Code:

```      |       |                *       |            *    *(4,4)       |          *      :       |          *        :       |                  :       |    (2,2)*        :       |        :        :       |        :        :       |        :        :     -+---------+----+----+------       |        2    3    4```

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

• January 9th 2007, 11:02 PM
talhaguy
thankyou so much guys, i really appreciate it.