True or False?

Algebra Level 3

f ( x ) = 1 ln ( log 1 e 2 e x ) \large f(x) =\frac { 1 }{ \ln { { (\log { \sqrt { 1-{ e }^{ 2-{ e }^{ x } } } } ) } } }

The domain of function f ( x ) f(x) above is ( ln 2 , + (\ln2,+\infty ).

True False

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1 solution

G Silb
Nov 12, 2018

The radicand is at most 1, therefore the square root is at most 1. The log of this is then less than or equal to zero, and undefined for ln.

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