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Q.
The maximum value of function $f(x)=\frac{|x|-2-x^2}{|x|+1}$, is
Complex Numbers and Quadratic Equations
Solution:
We have $f(x)=3+\left(\frac{|x|-2-x^2}{|x|+1}\right)-3=3-\frac{x^2+2|x|+5}{|x|+1}=3-\frac{(|x|+1)^2+4}{|x|+1}$
$=3-\left((|x|+1)+\frac{4}{|x|+1}\right) \leq 3-2 \sqrt{4}=3-4=-1$.