Find the range of `f(x) = sin^(-1) x + tan^(-1) x + cos^(-1) x`

1.	Find the range of `f(x) = sin^(-1) x + tan^(-1) x + cos^(-1) x`
Answer» Clearly, the domain of the function is `[-1, 1]` Also, `tan^(-1) x in [-(pi)/(4), (pi)/(4)] " for " x in [-1, 1]` Now, `sin^(-1) x + cos^(-1) x = (pi)/(2) AA x in [-1, 1]` Thus, `f(x) = tan^(-1) x + (pi)/(2)`, where `x in [-1, 1]` Hence, the range is `[-(pi)/(4) + (pi)/(2), (pi)/(4) + (pi)/(2)] = [(pi)/(4), (3pi)/(4)]`

Discussion

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