Rejection Method Generating Cauchy variables

Question

$$f(x)=\frac{e^x}{(1+e^x)^2}$$ $$g(x)=\frac{1}{2}e^{-\left | x \right |}$$ both for ($-\infty$$<x<$$\infty$).Why we can't use either f or g to sample from a Cauchy distribution. What's the reason for that ??And also whether either would provide a practically useful way of generating standard normal random variables??? Thanks in advance.