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  4. The domain and range of the relation R given by R= (x, y): y=x+(6/x); where x, y ∈ N and x < 6 is

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Q. 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

Relations and Functions

Solution:

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 $R=\left\{7, 5\right\}$