Find the range of `f(x)=|3tan^(-1)x-cos^(-1)(0)|-cos^(-1)(-1)dot`

Explanation

`f(x) = |3 tan^(-1) x - cos^(-1) (0)| - cos^(-1) (-1)`
`= |3 tan^(-1) x - (pi//2)| - pi`
Now, `-(pi)/(2) lt tan^(-1) x lt(pi)/(2)`
or `-(3pi)/(2) lt 3 tan^(-1) x lt (3pi)/(2)`
or `-2pi lt 3 tan^(-1) x-(pi)/(2) lt pi`
or `0 le |3 tan^(-1) x -(pi)/(2)| lt 2pi`
or `-pi |3 tan^(-1) x -(pi)/(2)| - pi lt pi`