### Relations and Functions

goals
Answer the questions on the basis of the function given below :
$\displaystyle f:(0, \infty) \rightarrow (-\frac {\pi}{2}, \frac {\pi}{2})$ be defined as, $\displaystyle f(x) = arc \: \tan( \: x)$
The total surface area, $\displaystyle S\ cm^2$, of a cylinder of radius r cm and height h cm, is given by the formula.
$\displaystyle S=2\pi rh+2\pi r^2$
Let a relation R be defined by
$\displaystyle R= \left \{ \left ( 4,5 \right ), \left ( 1,4 \right ), \left ( 4,6 \right ), \left ( 7,6 \right ), \left ( 3,7 \right ) \right \}.$ Find
$P(x)$ be polynomial of degree at most $5$ which leaves remainders $-1$ and $1$ upon division by $(x-1)^{3}$ and $(x+1)^{3}$ respectively
In the equation $y=kx+3$, $k$ is a constant. If $y=17$ when $x=2$, what is the value of $y$ when $x=4$?