Functions: If the domain of the function… | JEE Main 2025 | Yukti Vault

Yukti Vault

JEE Main 2025 (Online) 2nd April Evening ShiftQuestion 1

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

Functions

$26$✓ Correct answer$25$$29$$30$

Solution

$10+3x-x^2>0\Rightarrow-2<x<5$; $x+|x|>0\Rightarrow x>0$. Domain $(0,5)$, so $(1+0)^2+5^2=26$.

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