If the domain of the function f(x) = 1 a - x + ⁻¹ ( x - 1 b ) , where b > 0 , is [-2, 3) , then the value of a^2 + b^2 is equal to :

Step-by-step solution

For the function f(x) to be defined, both terms must be defined. 1) For the first term 1 a - x : a - x > 0 x So, x (- , a) 2) For the second term ⁻¹ ( x - 1 b ) : -1 x - 1 b 1 Since b > 0 , multiplying by b gives: -b x - 1 b 1 - b x 1 + b So, x [1 - b, 1 + b] The domain of f(x) is the intersection of these two intervals: x [1 - b, 1 + b] (- , a) We are given that the domain is [-2, 3) . Since the lower bound is closed, it must correspond to 1 - b . 1 - b = -2 b = 3 Since the upper bound is open, it must correspond