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

Explanation

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)]`