Types of Functions

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

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.

Are $f\left(x\right)=x^2$ and $g\left(x\right)=x^3$ are equal functions? Find the values of $f\left(4\right)$ and $g\left(4\right)$.

Are $f\left(x\right)=3x^2$ and $g\left(x\right)=3x^3$ are equal functions? Find the values of $f\left(3\right)$ and $g\left(3\right)$.

Are $f\left(x\right)=2x^2$ and $g\left(x\right)=2x^3$ are equal functions? Find the values of $f\left(2\right)$ and $g\left(2\right)$.

Are $f\left(x\right)=x^2$ and $g\left(x\right)=x^3$ are equal functions? Find the values of $f\left(3\right)$ and $g\left(3\right)$.

Are $f\left(x\right)=x^2$ and $g\left(x\right)=x^3$ are equal functions? Find the values of $f\left(2\right)$ and $g\left(2\right)$.

Solve the following when the value of $x=-5.5$

$\left|x-\sqrt{256}\right|+\left|x-28.5÷23\right|-\left|-38.90-16.7\right|=?$

Solve:

$\left|-20-8\right|+\left|-3.18-9.25\right|-\left|3.88-9.62\right|+\left|45.12+0.1\right|=?$