JEE Main 2026 · 6 Apr · Shift 2 · Mathematics Q1

MathematicsSingle correct+4 / -1Question 1 of 75

Let $f:\mathbf R\to\mathbf R$ be defined as $f(x)=\dfrac{2x^2-3x+2}{3x^2+x+3}$ . Then $f$ is :

both one-one and onto

one-one but not onto

onto but not one-one

neither one-one nor onto

Answer and worked solution

Official answer: D

Not one-one. Replacing x by $\tfrac1x$ :
$f\left(\tfrac1x\right)=\frac{2-3x+2x^2}{3+x+3x^2}=f(x),$
so for example $f(2)=f\left(\tfrac12\right)$ .

Not onto. The denominator is always positive and f is a bounded rational function (it tends to $\tfrac23$ ), so it cannot take every real value.

(D)

Topics:Types of functions

JEE Main 2026 · 6 Apr · Shift 2, Mathematics question 1