Special Functions and Their Graphs

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 $\text{x}\in \text{R}$.

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

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:

Define greatest integer function. Also draw its graph and write the domain and range of this function.

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.

Identify the graph of signum function $f\left(x\right)=2\frac{\left|x\right|}{x}$ and find whether the given signum function is odd or even.

Draw the graph of step function $y=\left[x\right]$ and find the value of $\left[-3.2\right]$.

Draw the graph of step function $y=\left[x\right]$ and find the value of $\left[-1\right]$.

Draw the graph of step function $y=\left[x\right]$ and find the value of $\left[-1.99\right]$.

Draw the graph of step function $y=\left[x\right]$ and find the value of $\left[1.99\right]$.

Draw the graph of step function $y=\left[x\right]$ and find the value of $\left[2.2\right]$.

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

$f\left(x\right)=4\frac{\left|x\right|}{x}$. State whether given function is even or odd.

$f\left(x\right)=3\frac{\left|x\right|}{x}$. State whether given function is even or odd.

$f\left(x\right)=2\frac{\left|x\right|}{x}$. State whether given function is even or odd.

State whether signum function is even or odd.

Draw the graph of signum function and state the discontinuous point of signum function.