TS EAMCET · Maths · Functions
If \(f(x)=\tan \left(\frac{\pi}{\sqrt{x+1}+4}\right)\) is a real valued function then the range of \(f\) is
- A \([-1,1]\)
- B \((0,1]\)
- C \([-1, \infty)\)
- D \(\mathbb{R}\)
Answer & Solution
Correct Answer
(B) \((0,1]\)
Step-by-step Solution
Detailed explanation
\(x+1 \ge 0 \Rightarrow x \ge -1\) \(\sqrt{x+1} \in [0, \infty)\) \(\sqrt{x+1}+4 \in [4, \infty)\) \(\frac{\pi}{\sqrt{x+1}+4} \in \left(0, \frac{\pi}{4}\right]\) \(\tan\left(\frac{\pi}{\sqrt{x+1}+4}\right) \in \left(\tan(0), \tan\left(\frac{\pi}{4}\right)\right]\)…
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