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

Options

A. `[(pi)/(2), pi)`
B. `[(pi)/(4), pi)`
C. `[(pi)/(6), pi)`
D. `[(pi)/(8), pi)`

Answer

B

Explanation

Let `theeta = cot^(-1) (2 x - x^(2))`, where `theta in (0, pi)`
`rArr cot theta = 2x - x^(2), " where" theta in (0, pi)`
`= 1- (1 - 2x + x^(2)), " where " theta in (0, pi)`
`= 1 - (1 - x)^(2), " where " theta in (0, pi)`
`rArr cot theta le 1, " where " theta in (0, pi)`
`rArr (pi)/(4) le theta le pi`
`rArr` Range of `f(x) "is " [(pi)/(4), pi)`