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  4. The smallest positive integral value of f ( x )=( x 2+ x +7/ x +2), x ∈ R is equal to

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Q. The smallest positive integral value of $f ( x )=\frac{ x ^2+ x +7}{ x +2}, x \in R$ is equal to

Relations and Functions - Part 2

Solution:

$y x+2 y=x^2+x+7$
$x^2+x(1-y)+7-2 y=0 \text { as } x \in R $
$D \geq 0 $
$(1-y)^2-4(7-2 y) \geq 0 $
$y^2+6 y-27 \geq 0 $
$(y+9)(y-3) \geq 0 $
$y \in(-\infty,-9] \cup[3 . \infty) $
$\therefore \text { Smallest positive value of } f(x) \text { is } 3$ .