If the domain of the function f(x)= _7(1- _4(x^2-9 x+18)) is (, ) (, o), then +++o is equa…

Question

If the domain of the function $f(x)=\log _7\left(1-\log _4\left(x^2-9 x+18\right)\right)$ is $(\alpha, \beta) \cup(\gamma, o)$, then $\alpha+\beta+\gamma+\hat{o}$ is equal to

Accepted Answer

$$\begin{aligned} & 1-\log _4\left(x^2-9 x+18\right)>0 \ & \log _4\left(x^2-9 x+18\right)<1 \ & x^2-9 x+18<4 \ & x^2-9 x+14<0 \ & x \in(2,7) \ & x^2-9 x+18>0 \ & x \in(-\infty, 3) \cup(6, \infty) \end{aligned}$$ $$\begin{aligned} & x \in(2,3) \cup(6,7) \ & \alpha+\beta+\gamma+\delta=18 \end{aligned}$$

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