Let f(x) = ⁻¹ ( 2x^2-a b ) + 1 _e(|x|-c) , where a, b, c R and b > 0 . If the domain of f(x) is [-5, -4) (4, 5] , then the value of a - 2b + c is equal to

Step-by-step solution

For the domain of f(x) , we require: 1) -1 2x^2-a b 1 -b 2x^2-a b a-b 2 x^2 a+b 2 2) |x|-c > 0 |x| > c 3) |x|-c 1 |x| c+1 The given domain is [-5, -4) (4, 5] , which can be written as 4 Comparing the upper bound of x^2 from the inverse sine function with the given domain: a+b 2 = 25 a+b = 50 The lower bound of the domain is determined by the logarithmic conditions and the lower bound of the inverse sine function. Since the interval is open at 4 , the excluded point must come from the base of the logarithm not being