Question

The domain and range of the relation R given by R $=\left\{(x,y):y=x+\frac{6}{x},\mathrm{where}x,y\in N\mathrm{and}x<6\right\}$ is

• A. $\left\{1,2,3\right\},\left\{7,5\right\}$
• B. $\left\{1,2\right\},\left\{7,5\right\}$
• C. $\left\{2,3\right\},\left\{5\right\}$
• D. None of these

Answer 1

The correct option is A

$\left\{1,2,3\right\},\left\{7,5\right\}$

Explanation for the correct option:

$R=\left\{(x,y):y=x+\frac{6}{x},\mathrm{where}x,y\in N\mathrm{and}x<6\right\}$

When $x=1,y=7\in N,so(1,7)\in R.$
When,$x=2,y=2+3=5\in N,so(2,5)\in R.$
For $x=3,y=3+2=5\in N,(3,5)\in R.$

For $x=4,y=4+\frac{6}{4}\notin N\text{and}forx=5,y=5+\frac{6}{5}\notin N.$
Therefore,$R=\left\{\right(1,7),(2,5),(3,5)\}$
∴ Domain of $R=\{1,2,3\}$ and Range of $R=\{7,5\}$

Hence,option(A) is correct answer.