Hi everybody, could anyone help me with this?:

Suppose that the function g has the following property:

$\displaystyle \forall{\epsilon>0}\wedge\forall{x}\quad 0<|x-2|<\epsilon^2\implies |g(x)-4|<\epsilon$

For each $\displaystyle \epsilon>0$ find a $\displaystyle \delta>0$ such that, for all x:

If $\displaystyle 0<|x-2|<\delta$, then $\displaystyle \left|\dfrac{1}{g(x)}-\dfrac{1}{4}\right|<\epsilon$

Well, I've started working here to find an expression for $\displaystyle \delta$ in terms of $\displaystyle \epsilon$:

$\displaystyle \left|\dfrac{1}{g(x)}-\dfrac{1}{4}\right|=\left|\dfrac{4-g(x)}{4g(x)}\right|=\dfrac{|4-g(x)|}{4|g(x)|}=\dfrac{|g(x)-4|}{4|g(x)|}$

Here I suppose I need to bound $\displaystyle g(x)$ but, how? If not, what's next?

Thanks in advance.