JEE Mains · Maths · STD 11- 2. Relation and Function
If the domain of the function \(f ( x )=\frac{[ x ]}{1+ x ^2}\), where \([x]\) is greatest integer \(\leq x\), is \((2,6)\), then its range is
- A \(\left(\frac{5}{26}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}\)
- B \(\left(\frac{5}{26}, \frac{2}{5}\right]\)
- C \(\left(\frac{5}{37}, \frac{2}{5}\right]-\left\{\frac{9}{29}, \frac{27}{109}, \frac{18}{89}, \frac{9}{53}\right\}\)
- D \(\left(\frac{5}{37}, \frac{2}{5}\right]\)
Answer & Solution
Correct Answer
(D) \(\left(\frac{5}{37}, \frac{2}{5}\right]\)
Step-by-step Solution
Detailed explanation
\(\begin{array}{ll}f(x)=\frac{2}{1+x^2} & x \in[2,3) \\ f(x)=\frac{3}{1+x^2} & x \in[3,4) \\ f(x)=\frac{4}{1+x^2} & x \in[4,5) \\ f(x)=\frac{5}{1+x^2} & x \in[5,6)\end{array}\) \(\left(\frac{5}{37}, \frac{2}{5}\right]\)
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