Types of Functions

For any real number x, the maximum value of $4–6x–x^2$ is ?

If $x$ is a negative real number, then

Solve the following where $\text{x}\in \text{R}$.

$2^{\left|\text{X}+2\right|}-\left|2^{\text{X}+1}-1\right|=2^{\text{x}+1}+1$

Solve the following where $\text{x}\in \text{R}$.

$\left|{\text{x}}^3+1\right|+{\text{x}}^2-\text{x}-2=0$

$x=\sqrt{a^{{\sin }^{-1}t}}, y=\sqrt{a^{{\cos }^{-1}t}}$,  what would be the value of $\frac{dy}{dx}$?

If  $f:R\to R$  is defined by  $f\left(x\right)=x^2-3x+2,$ The $f\left(f\left(x\right)\right),$ would be $$

The integral  ${\int }_0^{1.5}\left[x^2\right]dx,$ where $\left[.\right]$ denotes the greatest integer function, equals:

Let $f=\left\{\right(2,7),(3,4),(7,9),(-1,6),(0,2),(5,3\left)\right\}$ be a function from  $A=\{-1,0,2,3,5,7\}$ to $B=\{2,3,4,6,7,9\}$,find wether it is one-one and onto function or not

For $x$ in $[0, \pi /2),$ if ${\cot }^{-1}\left(\frac{\sqrt{3}\cos \left(x\right)-\sin \left(x\right)}{\cos \left(x\right)+\sqrt{3}\sin \left(x\right)}\right)=\frac{\pi }{3}$ then $x=$

The value of ${\sin }^{-1}\left(\sin \left(\frac{4\pi }{5}\right)\right)+{\cos }^{-1}\left(\cos \left(\frac{13\pi }{5}\right)\right)$ is equal to

The value of $2{\sec }^{-1}\left(2\right)+{cosec}^{-1}(-2)$ is equal to

If ${\tan }^{-1}\left(x\right)=y,$ then

Consider $f:N\to Z$ defined by $f\left(x\right)=x^2-1.$ Then

The total number of solutions $\theta \in [-3\pi ,3\pi ]$ of the equation ${\cos }^2\theta -\sin \theta +1=0$ is equal to

The maximum possible value of $3\cos \theta +4\sin \theta +5$ is equal to

The value of ${\sin }^{-1}\frac{1}{3}+{\sin }^{-1}\frac{2\sqrt{2}}{3}+{\sin }^{-1}\left(\sin \frac{3\pi }{5}\right)$ is equal to