If the domain of the function f(x)= _ (10 x²-17 x+7 ) (18 x²-11 x+1 ) is (- , a) (b, c) (d, )- e , then 90(a+b+c+d+e) equals:

Step-by-step solution

For f(x) = _ (10x^2-17x+7) (18x^2-11x+1) , we need: Base > 0 : 10x^2-17x+7 > 0 10(x-1)(x-7/10) > 0 x 1 Base 1 : 10x^2-17x+6 = 0 x = 1/2 or x = 6/5 Argument > 0 : 18x^2-11x+1 > 0 18(x-1/2)(x-1/9) > 0 x 1/2 Intersecting conditions 1 and 3: (- , 1/9) (1/2, 7/10) (1, ) Removing base = 1 points: x = 1/2 is already excluded; x = 6/5 (1, ) must be removed. Domain: (- , 1/9) (1/2, 7/10) (1, ) - 6/5 So a = 1/9, ; b = 1/2, ; c = 7/10, ; d = 1, ; e = 6/5 . 90(a+b+c+d+e) = 90 ( 1 9 + 1 2 + 7 10 +1+ 6 5 ) = 10+45+63+90+108 = 31