If the domain of the function f(x)=log_7 (1-log_4 (x^2-9x+18 ) ) is (alpha,beta)cup(gamma,delta) , then alpha+beta+gamma+delta is equal to

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JEE Main 2025 (Online) 3rd April Evening ShiftQuestion 1

If the domain of the function $f(x)=\log_7\left(1-\log_4\left(x^{2}-9x+18\right)\right)$ is $(\alpha,\beta)\cup(\gamma,\delta)$, then $\alpha+\beta+\gamma+\delta$ is equal to

Functions

$15$$16$$17$$18$✓ Correct answer

Solution

$x^2-9x+18>0$ and $\log_4(x^2-9x+18)<1\Rightarrow0<x^2-9x+18<4$ with $x<3$ or $x>6$. Hence $x\in(2,3)\cup(6,7)$, sum $=18$.

Functions - JEE Mathematics question (JEE Main 2025 (Online) 3rd April Evening Shift)

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