Question

Hello,

Is a math function always undefined if you divide by zero, even if there is a +3 after? Example:
(X/X-3)+3.

Answer 1

Trying to check if this function is defined at X = 3 ?

Answer 2

Yes, but i dont know if that 3 makes the function defined always.

Answer 3

It's not... lol, hang on, let me explain...

Answer 4

Suppose it IS defined...at x = 3.
Then we have a value for it, say k.
\[\Large k = \frac30 + 3\]
right?

Answer 5

Then we can subtract 3 from both sides
\[\Large k -3 = \frac30\]
And divide 3 from both sides
\[\Large \frac{k-3}3= \frac10\]
And suddenly, 1/0 has a value, which we know to be false...
thus,
\[\Large \frac{x}{x-3}+3\]
is undefined, even if there's a + 3

Answer 6

Thanks, got it!

Answer 7

@terenzreignz where did you get "a + 3" ?

Answer 8

sorry, 'a' here is the English indefinite article, not a variable...

I apologize for the ambiguity ^_^

Answer 9

Probably should have typed
a +3

Answer 10

or
a "+3"

Answer 11

Ahhh..a plus 3.

Answer 12

Nice work.

Answer 13

Note also that x = 3/0 is undefined because then we would be able to say that x * 0 = 3, which says that there is something that multiplies with 0 to give a three. But "0" added to itself "x" times is still zero and could never be 3. Zero has this unique property that x*0 = 0 for any x. So x/0 is undefined because x*0=3 is undefined. We even agree to say x=0/0 is undefined, although x*0 = 0 is defined. So anything divided by zero, stops us in our tracks and we are prohibited from using that value.