Q81 / 150 · MHT CET 2020 (16 Oct Shift 2) · Mathematics

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.
Correct answer
D
discontinuous at exactly one point.

Solution

(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. $x=0$.

Hence, the correct answer is option: 'D'.

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