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

The function $f(x) = \tan^{-1}(\sin x + \cos x)$ is an increasing function in the interval.....

If $f(x) = x$,$-1 \le x \le 1$,then the function $f(x)$ is

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:

If $f(x) = x e^{x(1 - x)}$,then $f(x)$ is

If $f(x)=x^3+a x^2+b x+5 \sin ^2 x$ is an increasing function on $R$,then