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

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Question

(C) The function $f(x) = \log |\log x|$ is defined if the argument of the outer logarithm is strictly positive,i.e.,$|\log x| > 0$,and the argument of

Vedclass · Accepted Answer

$(0, 1) \cup (1, \infty)$

Vedclass · Answer

(C) The function $f(x) = \log |\log x|$ is defined if the argument of the outer logarithm is strictly positive,i.e.,$|\log x| > 0$,and the argument of the inner logarithm is strictly positive,i.e.,$x > 0$.For $|\log x| > 0$,we must have $\log x 
eq 0$,which implies $x 
eq 1$.Combining the conditions $x > 0$ and $x 
eq 1$,we get the domain as $x \in (0, 1) \cup (1, \infty)$.

The domain of the function $f(x) = \log |\log x|$ is:

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