Question

Is the following statement true or false, and why?

If f(x) =x^2-4/x-2 and g(x)=x+2, then f and g are the same function.

Answer 1

Let me post a better solution.

Answer 2

Assume f(x) = g(x)
Let x = 2
Then f(2) = g(2)
False
Therefore f(x) ≠ g(x)

Answer 3

Hold on, I think I got it. You're saying that I can plug in any number and if they don't have the same outcome they can't be the same. Is that it??

Answer 4

Yes, correct.

Answer 5

Because you can try any other number except x = 2 and it will work.

Answer 6

My mind is blown at how easy that was, and you just came and... like nothing solved it. How would I answer the question though? Would I say "They are not the same because both functions have different outcomes"

Answer 7

Or im thinking of putting, "f(2)=x^2-4/x-2 ≠ g(x)=x-2"

Answer 8

No, the outcome would be the same for any other number except for x = 2. So they are the same with that one exception. f(x) has a discontinuity at x = 2. That's the only thing that makes them different. Another way to see it would be to graph both at the same time on your calculator.

Answer 9

That one exception is the only thing that makes f(x) and g(x) different.

Answer 10

Yeah, so by showing the exception I would be proving that they are not the same and answering the question. Correct?

Answer 11

Correct

Answer 12

Ok just to make sure now, "False, they are not the same because *show exception*"

Answer 13

Thank you very much.