Relations and Functions — MATHS STD 11 Science — Question

4. None of these.

Solution:

$\text{f(x)}=|\text{x}-1|$

Since, $|\text{x}^2-1|\neq|\text{x}-1|^2$

$\text{f(x)}^2\neq(\text{f(x)})^2$

Thus, (i) is wrong.

Since, $|\text{x}+\text{y}-1|\neq|\text{x}-1||\text{y}-1|$

$\text{f}(\text{x}+\text{y})\neq\text{f(x)}\text{f(y)}$

Thus, (ii) is wrong.

Since, $|\text{|x|}-1\neq||\text{x}-1||=|\text{x}-1|$

$\text{f(|x|)}\neq|\text{f(x)}|$

Thus, (iii) is wrong.

Hence, none of the given options is the answer.