Let f:mathbbR-\5\tomathbbR be defined as f(x)=(2x^2+3x-2)/(x-5) . Then f is

Sets, Relations and Function: Let f:mathbbR-\5\tomathbbR be defined as f(x)=(2x^2+3x-2)/(x-5) .… | JEE Main 2022

JEE Main 2022 (Online) 30th July Evening ShiftQuestion 1

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

Sets, Relations and Function

one-one and ontoone-one but not ontoonto but not one-oneneither one-one nor onto✓ Correct answer

Solution

Not onto: $y(x-5)=2x^2+3x-2\Rightarrow 2x^2+(3-y)x+5y-2=0$ has real $x$ iff $D=y^2-46y+25\ge0$, which fails for $y$ between the roots, so $f$ misses values. Not one-one: $f(\tfrac12)=f(-2)=0$ since $2x^2+3x-2=(2x-1)(x+2)$. Neither one-one nor onto. Option (D).

Sets, Relations and Function - JEE Mathematics question (JEE Main 2022 (Online) 30th July Evening Shift)

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