Question

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

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

Answer 1

Answer: (A)

When $x=1$, $y=7\in N$, so $(1,7)\in R$.
When, $x=2$, $y=2+3=5\in N$, so $(2,5)\in R$.
Again for $x=3$, $y=3+2=5\in N,(3,5)\in R$.
Similarly for $x=4$, $y=4+\frac{6}{4}\notin N$ for $x=5$, $y=5+\frac{6}{5}\notin N$.
Thus $R=\left\{\left(1,7\right),\left(2,5\right),\left(3,5\right)\right\}$,
$\therefore$ Domain of $R=\left\{1,2,3\right\}$ and Range of $R=\left\{7,5\right\}$