If the domain of the function f$(x) = 1 + 1$is (a, b), then$(1 + a) + b$is equal to : 2 2$\sqrt{10}$+3x-$x_{2}$$\sqrtx$+|x|
Step-by-Step Solution
Key Concept: Impose every domain restriction from logarithms, roots, denominators, and inverse functions before intersecting intervals.
$x + |x| > 0$$\Rightarrow$ x$\ in $(0,$\infty$) ...(1) (1) 2 &$10 + 3x - x > 0$2 $\Rightarrow$$x - 3x - 10 < 0$$\Rightarrow$ x$\ in $$(-2$, 5) ...(2) from (1)&(2) x$\ in $(0, 5) ∴$a = 0$&$b = 5$2 2 ∴$(1 + a$$) + b = 1 + 25 = 26$
Correct Answer: 1