lim as x approaches 4 g(x) = Infinity

Question

So I saw this equation on my test but I do not know what to do with this information. I tried to find problems like this but cannot find any, please help!

Answer 1

Ok, so it seems like the question might be asking that you define a function g(x) where the limit as x approaches 4 is infinity. If that is the case, a general answer would be g(x) equals to either, some function f(x) where the limit as x->4 is >0 divided by some h(x) where the limit as x->4 is 0⁺, or some function f(x) where the limit as x->4 is <0 divided by some h(x) where the limit as x-> 4 is 0^-. That however is the most general answer to the question. A simpler answer would a possible function of g(x). Something like g(x) = 1/|x-4| where f(x) = 1 and h(x)=|x-4|. Let me know how it turns out. if you need me to clarify any of this, please let me know.

Answer 2

Well, I'm not sure about your question, but maybe this will help:

f(x) = 1/(x-4)

as x approaches 4 f(x) becomes unbounded.

This is sometimes written lim x->4 f(x)=∞