AP EAMCET · Maths · Functions
The function \(f(x)=\operatorname{sech}(x)\) on \(\mathbf{R}\) has the range
- A \((0, \infty)\)
- B \((0,1]\)
- C \([1, \infty)\)
- D \((1, \infty)\)
Answer & Solution
Correct Answer
(B) \((0,1]\)
Step-by-step Solution
Detailed explanation
\(f(x)=\operatorname{sech} x\) \(=\frac{1}{\cosh x}=\frac{2}{e^x+e^{-x}}\) At \(\quad x=0, f(x)=\frac{2}{e^0+e^{-0}}=\frac{2}{2}=1\) At \(x \neq 0, f(x)\) is less than 1 or \(e^x+e^{-x}\) is greater than 2 . Also \(f(x) \neq 0\) at any value of \(x\). Hence, range…
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