Let [x] denote the greatest integer less than or equal to x . If the domain of the function f(x) = 1 [x]^2 - 5[x] + 6 + ⁻¹ ( 2x - 3 7 ) is [ , ) [ , ] , then the value of - + + is equal to

Step-by-step solution

For the domain of f(x) , we must satisfy two conditions: 1) The argument of the inverse cosine function must lie in [-1, 1] : -1 2x-3 7 1 -7 2x-3 7 -4 2x 10 -2 x 5 2) The expression inside the square root in the denominator must be strictly positive: [x]^2 - 5[x] + 6 > 0 ([x]-2)([x]-3) > 0 This implies [x] 3 . Since [x] is an integer, the inequalities become: [x] 1 x [x] 4 x 4 Taking the intersection of these conditions with x [-2, 5] : x ([-2, 5] (- , 2)) ([-2, 5] [4, )) x [-2, 2) [4, 5] Comparing this with the gi