f tan−1√3−sec−1(−2).

The given function is f(tan^(-1)√3 - sec^(-1)(-2)).

Step 1: Simplify the inverse trigonometric functions

tan^(-1)√3 = π/3 (since tan(π/3) = √3)

sec^(-1)(-2) = π - sec^(-1)(2) = π - π/3 = 2π/3 (since sec(π/3) = 2 and sec is negative in the second quadrant)

Step 2: Substitute the simplified values back into the function

f(π/3 - 2π/3) = f(-π/3)

Without knowing the specific form of the function f, we cannot simplify further. The final answer is f(-π/3).