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

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Verified by Experts

The correct Answer is:
`[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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