Which of the four statements given below is different from the others?

Let $f:(-1,1) \rightarrow \mathbb{R}$ be such that $f(\cos 4 \theta) = \frac{2}{2-\sec^2 \theta}$ for $\theta \in \left(0, \frac{\pi}{4}\right) \cup \left(\frac{\pi}{4}, \frac{\pi}{2}\right)$. Then the value$(s)$ of $f\left(\frac{1}{3}\right)$ is (are):

$f(x) = \frac{x}{\ln x}$ and $g(x) = \frac{\ln x}{x}$. Identify the $CORRECT$ statement.

Suppose $f:[-2,2] \rightarrow R$ is defined by $f(x) = \begin{cases} -1, & \text{for } -2 \leq x \leq 0 \\ x-1, & \text{for } 0 < x \leq 2 \end{cases}$. The set $\{x \in [-2,2] : x \leq 0 \text{ and } f(|x|) = x\}$ is equal to:

Which of the following statements is correct?

Let $f(x) = \sqrt{x}$ and $g(x) = x$ be two functions defined over the set of non-negative real numbers. Find $(f+g)(x)$,$(f-g)(x)$,$(fg)(x)$,and $(\frac{f}{g})(x)$.