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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