The range of the function f(x)= x |x| is: - Vidyadip

MCQ

The range of the function $\text{f(x)}=\frac{\text{x}}{|\text{x}|}$ is:

A
$R - \{0\}$
B
$R - \{-1, 1\}$
✓
$\{-1, 1\}$
D
None of these.

✓

Answer

Correct option: C.

$\{-1, 1\}$

$\text{f(x)}=\frac{\text{x}}{|\text{x}|}$
Let $\text{y}=\frac{\text{x}}{|\text{x}|}$
For $x > 0, |x| = x$
$\Rightarrow\text{y}=\frac{\text{x}}{\text{x}}=1$
For $x < 0, = -x$
$\Rightarrow\text{y}=\frac{\text{x}}{-\text{x}}=-1$
Thus, range of $f(x)$ is $\{-1, 1\}$

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