Q102 / 160 · TS EAMCET 2024 (10 May Shift 2) · Mathematics

The real valued function $f(x)=\frac{|x-a|}{x-a}$ is

  • A
    continuous only at $x=a$
  • B
    discontinuous only for $x \gt a$
  • Correct answer
    C
    a constant function when $x \gt a$
  • D
    strictly increasing when $x \lt a$

Solution

$\begin{aligned} & f(x)= \frac{|x-a|}{x-a} \\ &=\left\{\begin{array}{cc}1 & , \\ -x \gt a \\ -1 & , \\ x \lt a\end{array} \Rightarrow \lim _{x \rightarrow a} f(x) \text { doesn't exist }\right.\end{aligned}$ $\therefore f(x)$ is discontinuous at $x=a$ and constant when $x \gt a$ or $x \lt a$

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

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