For what values of $x$ is the function $f(x) = x^4 - 4x^3 + 4x^2 + 40$ monotonically decreasing?

The interval in which the function $f(x) = \operatorname{Tan}^{-1}(\sin x + \cos x)$ is an increasing function,is

Let $f(x) = e^x - x$ and $g(x) = x^2 - x$,$\forall x \in R$. Then the set of all $x \in R$,where the function $h(x) = (f \circ g)(x)$ is increasing is

Let $f : R \rightarrow R$ be a twice differentiable function such that $f^{\prime\prime}(x) > 0$ for all $x \in R$ and $f^{\prime}(a-1) = 0$,where $a$ is a real number. Let $g(x) = f(\tan^{2}x - 2\tan x + a)$,$0 < x < \frac{\pi}{2}$. Consider the following two statements:
$(I)$ $g$ is increasing in $(0, \frac{\pi}{4})$
$(II)$ $g$ is decreasing in $(\frac{\pi}{4}, \frac{\pi}{2})$
Then,

The equation $x^3+x-1=0$ has

The function $f(x) = \frac{x}{\log_x e}$ is increasing on the interval . . . . . . ,where $x \in \mathbb{R}^+ - \{1\}$.