Types of Functions

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 general value of  $\theta$ satisfying the equation  ${2\sin }^2\theta -3\sin \theta -2=0$ , is

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

Solve $\left|x-2\right|\ge 7, x\in R$

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

Let $f:R\to R$ and $f\left(x\right)=5x-7$, show that it is bijective.

Let $f:N\to Q$ and $f\left(x\right)=x^3$,find it is bijective or not.

If the period of the function $f\left(x\right)=\sin x+4\cos 2x$ is $x\mathrm{\pi }$, then find the value of $x$.

Let $f\left(x\right)={\log }_{0.5}\left(x^2-5x+6\right)$, then $f\left(x\right)$ is

Identify the graph of signum function $f\left(x\right)=5\frac{\left|x\right|}{x}$ and find whether the given signum function is odd or even.

Identify the graph of signum function $f\left(x\right)=4\frac{\left|x\right|}{x}$ and find whether the given signum function is odd or even.

Identify the graph of signum function $f\left(x\right)=3\frac{\left|x\right|}{x}$ and find whether the given signum function is odd or even.