JEE Main 2022 · 30 Jul · Shift 2 · Mathematics Q61

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MathematicsSingle correct+4 / -1Question 61 of 90

Let $f:\mathbb R-\{5\}\to\mathbb R$ be defined as $f(x)=\dfrac{2x^2+3x-2}{x-5}$ . Then $f$ is

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

Range. $f(x)=y$ gives $2x^2+(3-y)x+(5y-2)=0$ , real only when $y^2-46y+25\ge0$ ; values of y between the roots are missed, so f is not onto. A quadratic in x also has two roots for most y, so f is not one-one.

(D)

Topics:Types of functions

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JEE Main 2022 · 30 Jul · Shift 2, Mathematics question 61