Special Functions and Their Graphs

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.

If $f\left(x\right)=\frac{2x+3}{3x-2}, x\ne \frac{2}{3}$, then the function $fof$ is

Let $f\left(x\right)=\cos \left(ax\right)+\sin \left(x\right)$ be periodic. Then $a$ must be