The function $f(x) = 2x^3 - 9x^2 + 12x + 2$ is decreasing in

Assertion $(A)$: The function $f(x) = x - \log \left(\frac{1+x}{x}\right), x > 0$ has no maximum. Reason $(R)$: If a function $f(x)$ is strictly increasing in an interval $(a, b)$, then at any point in $(a, b)$, $f^{\prime}(x) \neq 0$. The correct option among the following is

If the function $f(x) = \sin x - \cos^2 x$ is defined on the interval $[-\pi, \pi]$,then $f$ is strictly increasing in the interval

The function $f(x) = x^2$ is increasing in the interval

If $g(x) = \frac{1}{6} f(3 x^2 - 1) + \frac{1}{2} f(1 - x^2), \forall x \in R$,where $f''(x) > 0, \forall x \in R$. Then $g(x)$ is increasing in the interval

For what interval is the function $f(x) = \sin x - \cos x$ strictly increasing?