If the domain of the function f(x)=1√10+3 x-x^2+1x+|x| is (a, b), then (1+a)^2+b^2 is equa…

Question

If the domain of the function $f(x)=\frac{1}{\sqrt{10+3 x-x^2}}+\frac{1}{\sqrt{x+|x|}}$ is $(a, b)$, then $(1+a)^2+b^2$ is equal to :

Accepted Answer

$$x+|x|= \begin{cases}2 x, & x \geq 0 \ 0, & x0$, as $2 x \neq 0

Similarly,

\end{cases}$$
\&\frac{1}{\sqrt{3 x+10-x\^2}} \text { is defined when } 3 x+10-x\^2>0\
\&
\Rightarrow \& x\^2-3 x-10

Solutions · 1