Relations and Functions · Question 18

If the domain of the function f(x) = 1 10 + 3x - x2 + 1 x + |x| is (a, b), then (1 + a)2 + b2 is equal to :

1. 29
2. 30
3. 25
4. 26

Answer

(4) 26

Solution

10 + 3x - x2 > 0 x2 - 3x - 10 < 0

(x - 5)(x + 2) < 0 -2 < x < 5

x + |x| > 0: for x 0, x + |x| = 0; for x > 0, x + |x| = 2x > 0 x > 0

domain = (0, 5) a = 0, b = 5

(1 + a)2 + b2 = 1 + 25 = 26

Answer: (4)