TS EAMCET · Maths · Continuity and Differentiability
The real valued function \(f(x)=\frac{|x-a|}{x-a}\) is
- A continuous only at \(x=a\)
- B discontinuous only for \(x \gt a\)
- C a constant function when \(x \gt a\)
- D strictly increasing when \(x \lt a\)
Answer & Solution
Correct Answer
(C) a constant function when \(x \gt a\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & f(x)= \frac{|x-a|}{x-a} \\ &=\left\{\begin{array}{cc}1 & , \\ -x \gt a \\ -1 & , \\ x \lt a\end{array} \Rightarrow \lim _{x \rightarrow a} f(x) \text { doesn't exist }\right.\end{aligned}\) \(\therefore f(x)\) is discontinuous at \(x=a\) and constant when…
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