Direction : Consider the following for the items that follow :

Let f(x) = |x|² - |x²|

Direction : Consider the following for the items that follow :

Let f(t) = $\rm \ln(t+\sqrt{1+t^2})$ and g(t) = tan(f(t)).  

Consider the following statements :

I. f(t) is an odd function.

Il. g(t) is an odd function.

Which of the statements given above is/are correct?  

If $f(x)=ax-b$ and $g(x)=cx+d$ are such that $f(g(x))=g(f(x))$, then which one of the following holds?

Which one of the following is correct in respect of $f(x) = \frac{1}{\sqrt{|x| - x}}$ and $g(x) = \frac{1}{\sqrt{x - |x|}}$?