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Find the range of the function f(x)=cot^...

Find the range of the function `f(x)=cot^(-1)(log)_(0. 5)(x^4-2x^2+3)`

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`y=(x^(2)-1)^(2)+2 ge 2`
or `log_(0.5)(x^(4)-2x^(2)+3) le -1`
or `cot^(-1)log_(0.5)(x^(4)-2x^(2)+3) in [(3pi)/(4),pi)`
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