If range of f(x) = frac{2x^2-14x^2-8x+49}{x^4-7x^2-4x+23} is ( a, b ], then ( a +b ) is

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1.Relation and Function

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If the range of $f(x) = \frac{2x^2-14x^2-8x+49}{x^4-7x^2-4x+23}$ is ($a, b$], then ($a +b$) is

A

$3$

B

$4$

C

$5$

D

$6$

Solution

$f(x)=2+\frac{3}{x^{4}-7 x^{2}-4 x+23}$

Let $h(x)=x^{4}-7 x^{2}-4 x+23$

$=\left(x^{2}-4\right)^{2}+(x-2)^{2}+3$

$h(x) \geq 3$

Range of $\mathrm{h}(\mathrm{x})$ is $[3, \infty)$

$\Rightarrow$ Range of $\mathrm{f}(\mathrm{x})$ is $(2,3]$

Standard 12

Mathematics

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