JEE Mains · Maths · STD 12 - 1. relation and function
The function \(f:R \to \left[ { - \frac{1}{2},\frac{1}{2}} \right],\) defined as \(f\left( x \right) = \frac{x}{{1 + {x^2}}}\) is
- A neither injective nor surjective
- B invertible
- C injective but not surjective
- D surjective not injective
Answer & Solution
Correct Answer
(D) surjective not injective
Step-by-step Solution
Detailed explanation
\((4)\) we have \(f:R \to \left[ { - \frac{1}{2},\frac{1}{2}} \right],\) \(f\left( x \right) = \frac{x}{{1 + {x^2}}}\forall x \in R\)…
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