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

Question

If the domain of the function $f(x)={\log }_{7}(1-{\log }_{4}({x}^{2}-9x+18))$ is $(\alpha ,\beta )\cup (\gamma ,o)$, then $\alpha +\beta +\gamma +\hat{o}$ is equal to

Accepted Answer

$\begin{gathered} 1-{\log }_{4}({x}^{2}-9x+18)>0 \ {\log }_{4}({x}^{2}-9x+18)0 \ x\in (-\infty,3)\cup (6,\infty) \end{gathered}$

$\begin{gathered} x\in (2,3)\cup (6,7) \ \alpha +\beta +\gamma +\delta =18 \end{gathered}$

Solutions · 1