Direction : Consider the following for the items that follow :

Let f(x) = |x|² - |x²|

Consider the following statements : 

I. f(x) is continuous at x = 0. 

Il. f(x) is continuous at x = 1 

Which of the statements given above is/are correct? 

Consider the following for the next two (02) items that follow:

Let $f(x) = \frac{x}{\ln x}; (x > 1)$

Consider the following statements :
1. $f(x)$ is increasing in the interval $(e, \infty)$
2. $f(x)$ is decreasing in the interval $(1, e)$
3. $9 \ln 7 > 7 \ln 9$
Which of the statements given above are correct ?

Consider the following for the next two (02) items that follow:

Let $f(x) = |x| + 1$ and $g(x) = [x] - 1$, where [.] is the greatest integer function.

Let $h(x) = \frac{f(x)}{g(x)}$.

What is $\lim\limits_{x \to 0-} h(x) + \lim\limits_{x \to 0+} h(x)$ equal to?

Consider the following for the next items that follow:

Let a function f be defined on ℝ - {0} and $\rm 2 f(x)+f\left(\frac{1}{x}\right)=x+3 $.