JEE Mains · Maths · STD 12 - 5. continuity and differentiation
Consider the function \(f:(0, \infty) \rightarrow R\) defined by \(f(x)=e^{-\left|\log _e x\right|}\). If \(m\) and \(n\) be respectively the number of points at which \(f\) is not continuous and \(f\) is not differentiable, then \(\mathrm{m}+\mathrm{n}\) is
- A \(0\)
- B \(3\)
- C \(1\)
- D \(2\)
Answer & Solution
Correct Answer
(C) \(1\)
Step-by-step Solution
Detailed explanation
\(f:(0, \infty) \rightarrow R\) \( f(x)=e^{-\left|\log _e x\right|}\) \(\mathrm{f}(\mathrm{x})=\frac{1}{\mathrm{e}^{\ln x \mid}}=\left\{\begin{array}{l}\frac{1}{\mathrm{e}^{-\ln x}} ; 0 < \mathrm{x} < 1 \\ \frac{1}{\mathrm{e}^{\ln x}} ; \mathrm{x} \geq 1\end{array}\right.\)…
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