MHB Give an example of a function f(x)

[alexmahone]

Give an example of a function $\displaystyle f(x)$ for which $\displaystyle f([-1,\ 1])=(-\infty,\ \infty)$.

My thoughts: $\displaystyle f(x)=\frac{x}{(x-1)(x+1)}$ is a function for which $f((-1,\ 1))=(-\infty,\ \infty)$.

 

[CaptainBlack]

Give an example of a function $\displaystyle f(x)$ for which $\displaystyle f([-1,\ 1])=(-\infty,\ \infty)$.

My thoughts: $\displaystyle f(x)=\frac{x}{(x-1)(x+1)}$ is a function for which $f((-1,\ 1))=(-\infty,\ \infty)$.

\(\displaystyle f(x)=\tan \left( \frac{x}{\pi/2} \right), \ \ x\in (-1,1) \)

will map \( (-1,1) \) to \( (-\infty, \infty) \) but \( [-1,1] \) might need a bit more thought, though you can just define \( f(-1)=f(1)=0 \)

CB