The function $f(x)=\frac{x+1}{9 x+x^{3}}$ is

The function $f(x)=\frac{x+1}{9 x+x^{3}}$ is
  1. discontinuous at exactly two points.
  2. continuous for all real values of $x$.
  3. discontinuous at exactly three points.
  4. discontinuous at exactly one point.

Solution

$f(x)=\frac{x+1}{9 x+x^{3}}=\frac{x+1}{x\left(9+x^{2}\right)}$ The function is discontinuous at exactly one point i.e. $x=0$.

Asked in: MHT CET 2020 (16 Oct Shift 2)

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