JEE Mains · Maths · STD 11- 2. Relation and Function
If the domain of the function \(f(x)=\log _7\left(1-\log _4\left(x^2-9 x+18\right)\right)\) is \((\alpha, \beta) \cup(\gamma, \delta)\), then \(\alpha+\beta+\gamma+\delta\) is equal to
- A \(18\)
- B \(16\)
- C \(15\)
- D \(17\)
Answer & Solution
Correct Answer
(A) \(18\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text { Domain } 1-\log _4\left(x^2-9 x+18\right) \gt 0 \\ & \text { Also } x^2-9 x+18 \gt 0 \\ & (x-3)(x-6) \gt 0\end{aligned}\) \(x \in(-\infty, 3) \cup(6, \infty)\) ...(1)…
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