Find the range of `f(x) = cot^(-1) (2x - x^(2))`

Explanation

`f(x)=cot^(-1)(2x-x^(2))`
`=cot^(-1)(1-(1-2x+x^(2)))`
`=cot^(-1)(1-(1-x)^(2))`
Now `-oo lt 1-(1-x)^(2) le 1 `
`implies cot^(-1)(-oo) gt cot^(-1)(1-(1-x)^(2)) ge cot^(-1)1`
`implies pi gt cot^(-1)(1-(1-x)^(2)) ge pi//4`
`implies f(x) in[(pi)/(4), pi)`
Thus, range is `[(pi)/(4), pi)`