JEE Mains · Maths · STD 11- 2. Relation and Function
Let \(f(x)=\frac{1}{7-\sin 5 x}\) be a function defined on \(R\). Then the range of the function \(f(x)\) is equal to:
- A \(\left[\frac{1}{8}, \frac{1}{5}\right]\)
- B \(\left[\frac{1}{7}, \frac{1}{6}\right]\)
- C \(\left[\frac{1}{7}, \frac{1}{5}\right]\)
- D \(\left[\frac{1}{8}, \frac{1}{6}\right]\)
Answer & Solution
Correct Answer
(D) \(\left[\frac{1}{8}, \frac{1}{6}\right]\)
Step-by-step Solution
Detailed explanation
\( \sin 5 x \in[-1,1] \) \( -\sin 5 x \in[-1,1] \) \( 7-\sin 5 x \in[6,8] \) \( \frac{1}{7-\sin 5 x} \in\left[\frac{1}{8}, \frac{1}{6}\right]\)
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