The domain and range of the relation R given by $\mathrm{R}=\left\{(x, y) / y=x+\frac{6}{x}, x, y \in…

The domain and range of the relation R given by $\mathrm{R}=\left\{(x, y) / y=x+\frac{6}{x}, x, y \in \mathrm{N}\right.$ and $\left.x < 6\right\}$ are
  1. Domain $=\{2,3\}$, Range $=\{5\} .$
  2. Domain $=\{1,2\}$, Range $=\{5,7\} .$
  3. Domain $=\{1,2,3,4,5\}$, Range $=\left\{7,5, \frac{6}{4}, \frac{6}{5}\right\} .$
  4. Domain \(=\{1,2,3,4,5\}\) and Range \(=\{7,5\}\)

Solution

$y=x+\frac{6}{x}, x, y \in N$ and $x < 6$ When $x=1, y=1+6=7$ When $x=2, y=2+3=5$ When $x=3, y=3+2=5$ When $x=4, y=4+1.5=5.5$ When $x=5, y=5+1.2=6.2$ Since $x, y \in N$ and $x < 6$, we write Domain $=\{1,2,3,4,5\}$ and Range $=\{7,5\}$

Asked in: MHT CET 2020 (20 Oct Shift 1)

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