jee-main 2017 Q77

jee-main · India · 02apr Composite & Inverse Functions Injectivity, Surjectivity, or Bijectivity Classification
The function $f : \mathbb{R} \rightarrow \left(-\dfrac{1}{2}, \dfrac{1}{2}\right)$ defined as $f(x) = \dfrac{x}{1 + x^2}$, is:
(1) Invertible
(2) Injective but not surjective
(3) Surjective but not injective
(4) Neither injective nor surjective 
The function $f : \mathbb{R} \rightarrow \left(-\dfrac{1}{2}, \dfrac{1}{2}\right)$ defined as $f(x) = \dfrac{x}{1 + x^2}$, is:\\
(1) Invertible\\
(2) Injective but not surjective\\
(3) Surjective but not injective\\
(4) Neither injective nor surjective
Paper Questions
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