Class 12 Relations And Functions · Mcq Single Correct1 Markstypes_of_functions
Class 12 Maths · Relations And Functions · Mcq Single Correct #96
The function \(f:\mathbb R\to\mathbb R\), \(f(x)=\frac{x}{1+|x|}\), is
✅ Step-by-Step Solution
Final Answer: Option (C): One-one but not onto
- The function is strictly increasing on either side of zero and across zero. On its image the inverse is \(x=y/(1-|y|)\), valid for exactly \(-1<y<1\). Thus the range is \((-1,1)\), and it is one-one but not onto \(\mathbb R\).
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