If f (x) is defined by $f(x)=\left\{\beg

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Target Exam

CUET

Subject

-- Mathematics - Section B1

Chapter

Continuity and Differentiability

Question:

If f (x) is defined by $f(x)=\left\{\begin{matrix}\frac{|x^2-2x|}{x^2-2x}&x≠0,2\\1&x=0\\-1&x=2\end{matrix}\right.$, then f is discontinuous at

Options:

–1 and 1

0 and 2

0 and 1

–2 and 2

Correct Answer:

0 and 2

Explanation:

$f(x)=\left\{\begin{matrix}1&x≤0\\-1&0<x≤2\\1&x>2\end{matrix}\right.$ Clearly f is discontinuous at 0 and 2 only.