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