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AP EAMCET · Maths · Functions

The domain of the real valued function \(f(x)=\log _2 \log _3 \log _5\left(x^2-5 x+11\right)\) is

  1. A \((2, \infty)\)
  2. B \((-\infty, 3)\)
  3. C \((2,3)\)
  4. D \((-\infty, 2) \cup(3, \infty)\)
Verified Solution

Answer & Solution

Correct Answer

(D) \((-\infty, 2) \cup(3, \infty)\)

Step-by-step Solution

Detailed explanation

\(\begin{aligned} & \text { } \log _3 \log _5\left(x^2-5 x+11\right)\gt0 \\ & \Rightarrow \log _5\left(x^2-5 x+11\right)\gt1 \Rightarrow(x-3)(x-2)\gt0 \\ & \Rightarrow x \in(-\infty, 2) \cup(3, \infty)\end{aligned}\)