Nice rooted lawn (ln)

Algebra Level 3

The domain of definition of function f ( x ) = ln ⁡ ∣ x ∣ − 1 ( x 2 + 4 x + 4 ) f(x) = \sqrt{\ln_{|x|-1} (x^2+4x+4)} is

none of them ( − 2 , − 1 ) ∪ [ 2 , ∞ ) (-2,-1) \cup [2,\infty) ( − 3 , − 1 ) ∪ [ 1 , ∞ ) (-3,-1) \cup [1,\infty) ( − 2 , − 1 ) ∪ [ 2 , 3 ) (-2,-1) \cup [2,3) ( − ∞ , 3 ] ∪ ( − 2 , − 1 ) ∪ ( 2 , ∞ ) (-\infty,3] \cup (-2,-1) \cup (2,\infty) ( − ∞ , − 1 ) ∪ [ 2 , ∞ ) (-\infty,-1) \cup [2,\infty)

Atul Shivam by Atul Shivam , 23, India

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1 solution

Manav Kumar
Mar 22, 2020

why not (1,2) , as, if (-2,-1) is included where base becomes positive, then why not (1,2) because in that case |x|-1 will still yield positive values and will act as same as that of (-1,-2). and for all these (x+2)^2 is always positive

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