Relations and Functions

Let $$f: A\rightarrow B, g: B\rightarrow C$$ and $$h:C\rightarrow D$$ be three functions, then the function $$gof:A \rightarrow C$$ defined by gof(x) g[f(x)] for all $$x \epsilon A$$ is called the composition of f and g.
Express $$R={(x, y) , y=3x, x\in (1, 2, 3) \text{ and }y \in (3, 6, 9, 12)}$$ as a set of ordered  pair.
Find period of $$\dfrac{{1 + \sin x}}{{\cos x\left( {1 + \cos ec\,x} \right)}}$$
The diagram below shows an equilateral triangle PQR of sides 6 cm. PM is

the line joining the midpoint of QR to P. N is a point on PM.
Mark the intersection of the two loci X and Y with the symbol
Given that $$f(x) = {\left( {a - {x^n}} \right)^{\cfrac{1}{n}}};2 > 0,n \in N$$, show that $$f\left( {f(x)} \right) = x$$.