If $f(x) = \log \left( \frac{1 + x}{1 - x} \right)$,then $f(x)$ is

If $f(x) = \cos([\pi^2]x) + \cos([- \pi^2]x)$,then which of the following is true?

Let the function $g : (-\infty, \infty) \to \left( - \frac{\pi}{2}, \frac{\pi}{2} \right)$ be given by $g(u) = 2 \tan^{-1}(e^u) - \frac{\pi}{2}$. Then,$g$ is -

Let $R$ be the set of real numbers. Define the real function $f: R \rightarrow R$ by $f(x) = x + 10$ and sketch the graph of this function.

Which of the following functions is an even function?

Assertion $(A)$: $\coth x = \frac{1-k}{1+k}$ where $0 < k < 2$.
Reason $(R)$: The graph of $y = \tanh x$ always lies between the lines $y = -1$ and $y = 1$.
Choose the correct option: