Question

Find the domain and range of the relation $R$ given by$R=(x,y):y=x+\frac{6}{x};wherex,y\in N\$and\$x<6$.

Answer 1

For $y,x$ can be satisfied for all value of $x$ but not for $0.$

Hence $x\in R-\left\{0\right\}$

Now $AM\ge GM$

$⟹\frac{x+\frac{6}{x}}{2}\ge \sqrt{x\times \frac{6}{x}}$

$⟹x+\frac{6}{2}\ge 2\sqrt{6}$

$\therefore y\in [2\sqrt{6},\infty ].$