TS EAMCET · Maths · Continuity and Differentiability
If \(f(x)=\left\{\begin{array}{cc}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, & -1 \leq x < 0 \ \frac{2 x+1}{x-2}, & 0 \leq x \leq 1\end{array}\right.\) is continuous on \([-1,1]\), then \(p=\)
- A \(-\frac{1}{2}\)
- B \(-\frac{1}{4}\)
- C \(\frac{1}{2}\)
- D 2
Answer & Solution
Correct Answer
(A) \(-\frac{1}{2}\)
Step-by-step Solution
Detailed explanation
\(f(x)=\left\{\begin{array}{c}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x},-1 \leq x < 0 \\ \frac{2 x+1}{x-2}, 0 \leq x \leq 1\end{array}\right.\) Continues in \([-1,1]\), so it is continues at \(x=0\) also So,…
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