Search any question & find its solution
Question:
Answered & Verified by Expert
The range of the function $f(x)=\frac{x}{1+|x|}, x \in R$, is
Options:
Solution:
2835 Upvotes
Verified Answer
The correct answer is:
$(-1,1)$
$(-1,1)$
$f(x)=\frac{x}{1+|x|}, x \in R$
If $x>0,|x|=x \Rightarrow f(x)=\frac{x}{1+x}$ which is not defined for $x=-1$
If $x < 0,|x|=-x \Rightarrow f(x)=\frac{x}{1-x}$ which is not defined for $x=1$ Thus $f(x)$ defined for all values of $\mathrm{R}$ except 1 and $-1$
Hence, range $=(-1,1)$.
If $x>0,|x|=x \Rightarrow f(x)=\frac{x}{1+x}$ which is not defined for $x=-1$
If $x < 0,|x|=-x \Rightarrow f(x)=\frac{x}{1-x}$ which is not defined for $x=1$ Thus $f(x)$ defined for all values of $\mathrm{R}$ except 1 and $-1$
Hence, range $=(-1,1)$.
Looking for more such questions to practice?
Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.