What type of function is $f(x) = \frac{x - 2}{x + 1}$,where $x \neq -1$?

For which value of $x$ is the function $f(x) = x^2 - 2x$ decreasing?

Let $(2, 3)$ be the largest open interval in which the function $f(x) = 2 \log_e(x-2) - x^2 + ax + 1$ is strictly increasing and $(b, c)$ be the largest open interval in which the function $g(x) = (x-1)^3(x+2-a)^2$ is strictly decreasing. Then $100(a+b-c)$ is equal to:

$f(x) = x^2 - 6x + 10$ is an increasing function in the . . . . . . interval.

Consider the following statements $S$ and $R$:
$S$: Both $\sin x$ and $\cos x$ are decreasing functions in $\left( \frac{\pi}{2}, \pi \right)$.
$R$: If a differentiable function decreases in $(a, b)$,then its derivative also decreases in $(a, b)$.
Which of the following is true?

Let $\lambda^{*}$ be the largest value of $\lambda$ for which the function $f_{\lambda}(x) = 4\lambda x^{3} - 36\lambda x^{2} + 36x + 48$ is increasing for all $x \in \mathbb{R}$. Then $f_{\lambda^{*}}(1) + f_{\lambda^{*}}(-1)$ is equal to: