Consider (where denotes greatest integer function.) If domain of is and the range of is

MATHEMATICS · Subjective · AP · AP Precalculus · Trigonometric and Polar Functions · Trigonometric and Polar Functions

Problem

Consider

f(x) = \sin^{-1}[2x] + \cos^{-1}([x] - 1)

(where

[.]

denotes greatest integer function.) If domain of

f(x)

[a, b]

and the range of

f(x)

{c, d}

, then

a + b + \frac{2d}{c}

is equal to (where

c < d

)