Continuous Extension of f(x) = (x^2 - 2)/(x^4 - 5x^2 + 6)

[distill3dkarnage]

Consider the function

. How should f(x) be defined at

to be continuous there? Give a formula for the continuous extension of f(x) that includes

in its domain.

F(x) = _____

I haven't the slightest idea how to approach this. Do I just edit the original function somehow? This whole idea of changing a function to suit your own needs seems a bit sketchy to me. I've always been skeptical about doing what you want to something mathematic to make it work for you, as I'm paranoid it violates some sort of math rule and can't "really" be done. Either way... any tips on how to start this thing?

 

[daon]

Re: Continuous Extension...?

Factor the numerator and denominator and cancel out the trouble maker(s). From there, evaluate the value in question inside your new function.

This whole idea of changing a function to suit your own needs seems a bit sketchy to me. I've always been skeptical about doing what you want to something mathematic to make it work for you, as I'm paranoid it violates some sort of math rule and can't "really" be done. Either way... any tips on how to start this thing?

You're not "making it work," you're finding a new function all together that works "better" for a certain model. In reality all one would need to do is evaluate the limit, not find a new function. Usually, plugging in is a heck of a lot easier than evaluating a limit, though.

 

[distill3dkarnage]

Re: Continuous Extension...?

Thank you!

The program is online, and since it was asking for an equation, the correct answer was the new function I got after factoring/canceling (i.e. no need to plug in x).

But thanks for that starting push! Haha :]

 

[daon]

Re: Continuous Extension...?

Thank you!

The program is online, and since it was asking for an equation, the correct answer was the new function I got after factoring/canceling (i.e. no need to plug in x).

But thanks for that starting push! Haha :]

No problem... but that wasn't the question you asked :wink: (at least not the whole thing)