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Question: Answered & Verified by Expert
If $f(x)=\left\{\begin{array}{r}x-1, x \lt 0 \\ \frac{1}{4}, x=0 \\ x^2, x\gt0\end{array}\right.$ then
MathematicsContinuity and DifferentiabilityJEE Main
Options:
  • A $\lim _{x \rightarrow 0^{+}} f(x)=1$
  • B $\lim _{x \rightarrow 0^{-}} f(x)=1$
  • C $f(x)$ is discontinuous at $x=0$
  • D None of these
Solution:
2644 Upvotes Verified Answer
The correct answer is: $f(x)$ is discontinuous at $x=0$
Clearly from curve drawn of the given function $f(x)$ is discontinuous at $x=0$.

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