If the domain of the function f x = cos - 1 x 2 - x + 1 sin - 1 2 x - 1 2 is the interval ( α , β ] , then α + β is equal to:

Step-by-step solution

Given function is f x = cos - 1 x 2 - x + 1 sin - 1 2 x - 1 2 For, sin - 1 x   &   cos 1 x to be defined - 1 ≤ x ≤ 1 and for f x to be defined f x ≥ 0 and the denominator of any expression can never be zero. Thus, to define the domain of the given function, we have - 1 ≤ x 2 - x + 1 ≤ 1 ,   x 2 - x + 1 ≥ 0 and sin - 1 2 x - 1 2 > 0 Taking the common values and using the range of sin - 1 x i.e. for positive values 0 < sin - 1 x ≤ π 2 , we get