If the domain of the function f(x) = _ (0.6) ( | 2x-5 x^2-4 | ) is (- , a] b [c, d) (e, ) , then the value of a + b + c + d + e is _______.

Step-by-step solution

For the function f(x) = _ 0.6 ( | 2x-5 x^2-4 | ) to be defined, two conditions must be satisfied: 1. The argument of the logarithm must be strictly positive: | 2x-5 x^2-4 | > 0 2x - 5 0 x 5 2 Also, the denominator cannot be zero: x^2 - 4 0 x 2 2. The expression inside the square root must be non-negative: _ 0.6 ( | 2x-5 x^2-4 | ) 0 Since the base of the logarithm is 0.6 | 2x-5 x^2-4 | (0.6)^0 | 2x-5 x^2-4 | 1 Since both sides are non-negative, we can square both sides: (2x-5)^2 (x^2-4)^2 (x^2-4)^2 - (2x-5)^2 0 Usin