The domain of the real valued function f(x) = | vedclass

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(D) For the function $f(x) = \log_2 \log_3 \log_5(x^2 - 5x + 11)$ to be defined,we require: $1$. $\log_5(x^2 - 5x + 11) > 0$ $\Rightarrow x^2 - 5x + 1

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

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(D) For the function $f(x) = \log_2 \log_3 \log_5(x^2 - 5x + 11)$ to be defined,we require: $1$. $\log_5(x^2 - 5x + 11) > 0$ $\Rightarrow x^2 - 5x + 11 > 5^0 = 1$ $\Rightarrow x^2 - 5x + 10 > 0$. Since the discriminant $D = (-5)^2 - 4(1)(10) = 25 - 40 = -15 $2$. $\log_3 \log_5(x^2 - 5x + 11) > 0$ $\Rightarrow \log_5(x^2 - 5x + 11) > 3^0 = 1$ $\Rightarrow x^2 - 5x + 11 > 5^1 = 5$ $\Rightarrow x^2 - 5x + 6 > 0$. Factoring the quadratic: $(x - 2)(x - 3) > 0$. This inequality holds when $x \in (-\infty, 2) \cup (3, \infty)$.

The domain of the real valued function $f(x) = \log_2 \log_3 \log_5(x^2 - 5x + 11)$ is

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