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NDA 2017
Exam
NDA
Year
2017
Subject
Mathematics
Chapter
Continuity and Differentiability

NDA 2017 · Mathematics · Continuity and Differentiability

Let f(x) be defined as follows : f(x)= cases 2 x+1, & -3 < x < -2...

Let f(x)f(\mathrm{x}) be defined as follows : f(x)=f(x)=\begin{cases}2 \mathrm{x}+1, & -3 < \mathrm{x} < -2 \\ \mathrm{x}-1, & -2 \leq \mathrm{x} < 0 \\ \mathrm{x}+2, & 0 \leq \mathrm{x} < 1\end{cases}$$ Which one of the following statements is correct in respect of the above function?

Options

  1. AIt is discontinuous at x=−2\mathrm{x}=-2 but continuous at every other point.
  2. BIt is discontinuous at x=−2\mathrm{x}=-2 but continuous at every other point.
  3. CIt is discontinuous at x=0\mathrm{x}=0 but continuous at every other point.
  4. DIt is discontinuous at every point.

Correct answer

C. It is discontinuous at x=0\mathrm{x}=0 but continuous at every other point.

Step-by-step solution

f(x)=\left\{2x+1,−3<x<−2x−1,−2≤x<0x+2,0≤x<1\begin{array}{cc} 2 x+1, & -3 < x < -2 \\ x-1, & -2 \leq x < 0 \\ x+2, & 0 \leq x < 1 \end{array}\right. Here, f(0−)=−1f\left(0^{-}\right)=-1 and f(0+)=2\mathrm{f}\left(0^{+}\right)=2 So, f(x)\mathrm{f}(\mathrm{x}) is discontinuous at x=0\mathrm{x}=0 and continuous at other points.
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