Functions

If $\mathrm{f}\left(\mathrm{x}\right)=\left\{\begin{array}{cc}{3}^{-\mathrm{x}}-1,& \mathrm{for} -1\le \mathrm{x}<0\\ \tan (\raisebox{1ex}{$\mathrm{x}$}\!\left/ \!\raisebox{-1ex}{$2)$}\right.,& \mathrm{for} 0\le \mathrm{x}<\mathrm{\pi }\\ \frac{\mathrm{x}}{{\mathrm{x}}^2-2},& \mathrm{for} \mathrm{\pi }\le \mathrm{x}\le 6\end{array}\begin{array}{}\end{array}\right.$, then $\sqrt{\mathrm{f}\left(0\right)+\mathrm{f}\left(\raisebox{1ex}{$\mathrm{\pi }$}\!\left/ \!\raisebox{-1ex}{$6$}\right.\right)+\frac{1}{5}\mathrm{f}\left(5\right)-\frac{1}{23}}=$

Define bounded function and find the bounded values of $y=\sin x+\cos x$.

Define bounded function and find the bounded values of $y=\cos 2x$.

Define bounded function and find the bounded values of $y=\sin 2x$.

Define bounded function and find the bounded values of $y=\cos x$.

Define bounded function and find the bounded values of $y=\sin x$.

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 $g\left(2\right)$.

If $f$ and $g$are real functions defined by $f\left(x\right)=x+7$ and $g\left(x\right)=3x+5$, then find the value of $f\left(3\right)-g\left(2\right)$.

The diagram shows the graph of a relation $R$ that maps set $A$ onto set $B$.

Explain why $R$ is a function from $A$ to $B$.

The number of cells in a culture, $N,t$ hours after it has been established is shown in the graph for $0\le t\le 20$.

The relation represented in the graph is a function. Give reasons why this is the case.

Determine whether relation given below is a function or not. If it is not a function, state the reason why.

$x=-3$

Determine whether relation given below is a function or not. If it is not a function, state the reason why.

$x=-3$

Determine whether straight line given below represents a function or not. If it is not a function, state the reason why.

$y=4$

Determine whether straight line given below represents a function or not. If it is not a function, state the reason why.

$y=4$

Determine whether straight line given below represents a function or not. If it is not a function, state the reason why.

$y=-x$

Determine whether straight line given below represents a function or not. If it is not a function, state the reason why.

$y=-x$