The range of the function f(x) = x 1 + | x | , ,x R, is - Vidyadip

MCQ

The range of the function $f(x) = \frac{x}{{1 + \left| x \right|}},\,x \in R,$ is

A
$R$
✓
$(-1,1)$
C
$R-\{0\}$
D
$[-1,1]$

✓

Answer

Correct option: B.

$(-1,1)$

b
$f\left( x \right) = \frac{x}{{1 + \left| x \right|}},x \in R$

If $x > 0,\left| x \right| = x \Rightarrow f\left( x \right) = \frac{x}{{1 + x}}$

which is not defined for $x=-1$

If $x < 0,\left| x \right| = - x \Rightarrow f\left( x \right) = \frac{x}{{1 - x}}$

which is not defined for $x=1$

Thus $f\left( x \right)$ defined for all value of $R$ except $1$ and $-1$

Hence, range $=(-1,1)$.

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