JEE Main 2017 · 2 Apr · Shift 1 · Mathematics Q61

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The function $f:\mathbb R\to\left[-\dfrac12,\dfrac12\right]$ defined as $f(x)=\dfrac x{1+x^2}$ , is :

injective but not surjective.

surjective but not injective.

neither injective nor surjective.

invertible.

Answer and worked solution

Official answer: B

$f(2)=f\left(\frac12\right)=\frac25$ , so $f$ is not injective. Since $|x|\le\frac{1+x^2}2$ , the range is exactly $\left[-\frac12,\frac12\right]$ , so $f$ is surjective.

Topics:Types of functions

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JEE Main 2017 · 2 Apr · Shift 1, Mathematics question 61