TS EAMCET · Maths · Continuity and Differentiability
The set of values of \(x\) for which the function \(f(x)=\log \left(\frac{x-1}{x+2}\right)\) is continuous, is
- A \(R\)
- B \((-\infty,-2) \cup(0, \infty)\)
- C \((-\infty,-2) \cup(1, \infty)\)
- D \((-2,-1)\)
Answer & Solution
Correct Answer
(C) \((-\infty,-2) \cup(1, \infty)\)
Step-by-step Solution
Detailed explanation
We have, \[ f(x)=\log \left(\frac{x-1}{x+2}\right) \] \(f(x)\) is continuous of \[ \begin{aligned} \frac{x-1}{x+2}>0 \Rightarrow(x-1)(x+2)>0 \\ \therefore x \in(-\infty,-2) \cup(1, \infty) \end{aligned} \]
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