The domain of the function f(x) = ⁻¹(x-2) 6 + [x] - [x]^2 + _ |x| (4-x) , where [x] denotes the greatest integer less than or equal to x , is

Step-by-step solution

For the function f(x) to be defined, each term must be defined. For ⁻¹(x-2) , we require: -1 x-2 1 1 x 3 For the denominator 6 + [x] - [x]^2 , the expression inside the square root must be strictly positive: 6 + [x] - [x]^2 > 0 [x]^2 - [x] - 6 ([x]-3)([x]+2) -2 Since [x] is an integer, [x] -1, 0, 1, 2 . This implies -1 x For the logarithmic term _ |x| (4-x) , the argument must be positive and the base must be positive and not equal to 1: 4-x > 0 x |x| > 0 x 0 |x| 1 x 1, -1 Taking the intersection of all these condi