MHT CET · Maths · Continuity and Differentiability
The function \(f(x)=\frac{x+1}{9 x+x^{3}}\) is
- A discontinuous at exactly two points.
- B continuous for all real values of \(x\).
- C discontinuous at exactly three points.
- D discontinuous at exactly one point.
Answer & Solution
Correct Answer
(D) discontinuous at exactly one point.
Step-by-step Solution
Detailed explanation
(C)
\(f(x)=\frac{x+1}{9 x+x^{3}}=\frac{x+1}{x\left(9+x^{2}\right)}\)
The function is discontinuous at exactly one point i.e. \(x=0\).
\(f(x)=\frac{x+1}{9 x+x^{3}}=\frac{x+1}{x\left(9+x^{2}\right)}\)
The function is discontinuous at exactly one point i.e. \(x=0\).
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