MHT CET · Maths · Functions
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
- A Domain \(=\{2,3\}\), Range \(=\{5\} .\)
- B Domain \(=\{1,2\}\), Range \(=\{5,7\} .\)
- C Domain \(=\{1,2,3,4,5\}\), Range \(=\left\{7,5, \frac{6}{4}, \frac{6}{5}\right\} .\)
- D Domain \(=\{1,2,3\}\), Range \(=\{5,7\} .\)
Answer & Solution
Correct Answer
(D) Domain \(=\{1,2,3\}\), Range \(=\{5,7\} .\)
Step-by-step Solution
Detailed explanation
\(y=x+\frac{6}{x}, x, y \in N\) 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 \(=\{7,5\}\)
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 \(=\{7,5\}\)
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