Lisantiom

Lisantiom

Answered

2022-10-03

Determine the natural domain of f ( x ) = N + 3 x 2 log ( x )

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Answer & Explanation

falwsay

falwsay

Expert

2022-10-04Added 8 answers

For the square root to yield real numbers it must hold that
x 2 N + 3 ,
meaning
x [ N + 3 ; N + 3 ] .
Now consider the denominator. First of all, the natural logarithm must take in positive values of x, so x > 0. Besides that, the denominator cannot be 0. The logarithm assumes that value at x = 1
Now what you do is the intersection of all of these constraints to obtain your domain.
x [ N + 3 ; N + 3 ] ( 0 ; 1 ) ( 1 ; ) .
Finally
x ( 0 ; N + 3 ] { 1 } .
If N is such that the square root stays below 1, the set substraction operation will just yield the interval ( 0 ; N + 3 ]

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