Find the smallest and the largest values of `tan^(-1) ((1 - x)/(1 + x)), 0 le x le 1`

Find the smallest and the largest values of `tan^(-1) ((1 - x)/(1 + x)

1.	Find the smallest and the largest values of `tan^(-1) ((1 - x)/(1 + x)), 0 le x le 1`
Answer» Correct Answer - `[0, (pi)/(4)]` `f(x) = tan^(-1).((1 - x)/(1 + x)), 0 le x le 1` ltbr gt Now `(1 - x)/(1 + x) = (2)/(1 + x) - 1` Given `0 le x le 1`, `rArr (2)/(1 + x) -1 in [0,1]` `rArr tan^(-1).((1 - x)/(1 + x)) in [tan^(-1) 0, tan^(-1) 1] " or " [0, (pi)/(4)]`

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