Indicate all correct alternatives if, `f(x) = x/2-1`, then on the interval `[0, pi]`

Options

A. `tan[f(x)]" where "[.]` is the greatest integer function, and `(1)/(f(x))` are both continuous.
B. `tan[f(x)]`, where [.] is the greatest integer function, and `f^(-1)(x)` are both continuous.
C. `tan[f(x)]`, where [.] is the greatest integer function, and `(1)/(f(x))` are both discontinuous.
D. `tan[f(x)]` where [.] is the greatest integer function, is discontinuous but `(1)/(f(x))` is continuous.

Answer

C

Explanation

`f(x)=(x)/(2)-1," "[0,pi]`
`tan.f(x)=tan((x)/(2)-1)`
`(1)/(f(x))=(1)/((x)/(2)-1)` is discontinuous at x=2
tan.f(x) is discontinuous for `x=2" in "[0,pi]`