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JEE Main 20253 AprilEvening Shift
Exam
JEE Main
Year
2025
Date
3 April
Shift
Evening Shift
Subject
Mathematics
Chapter
Functions

JEE Main 2025 · 3 April · Evening Shift · Mathematics · Functions

If the domain of the function f(x)= _7 (1- _4 (x^2-9 x+18)) is (α,...

If the domain of the function f(x)=log⁡7f(x)=\log _7\left(1-\log _4\left(x^2-9 x+18\right)\right) is (α,β)∪(γ,δ)(\alpha, \beta) \cup(\gamma, \delta), then α+β+γ+δ\alpha+\beta+\gamma+\delta is equal to

Options

  1. A1818
  2. B1616
  3. C1515
  4. D1717

Correct answer

A. 1818

Step-by-step solution

 Domain 1−log⁡4(x2−9x+18)>0 Also x2−9x+18>0(x−3)(x−6)>0\begin{aligned} & \text{ Domain } 1-\log _4\left(x^2-9 x+18\right) > 0 \\ & \text{ Also } x^2-9 x+18 > 0 \\ & (x-3)(x-6) > 0\end{aligned}x \in(-\infty, 3) \cup(6, \infty)...(1)...(1) also x2−9x+18<4x2−9x+14<0\begin{aligned} & \text{ also } x^2-9 x+18 < 4 \\ & x^2-9 x+14 < 0\end{aligned}x∈(2,7)x \in(2,7) ...(2)(1)∩(2)(2,3)∪(6,7)=(α,β)∪(γ,δ)⇒α+β+γ+δ=18\begin{aligned} & (1) \cap(2) \quad(2,3) \cup(6,7)=(\alpha, \beta) \cup(\gamma, \delta) \\ & \Rightarrow \alpha+\beta+\gamma+\delta=18\end{aligned}
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