SOLUTION: Find the domain of the function. h(x) = ln[(x^2)/(x-4)] What I have tried on the problem so far is as follows: [(x^2)/(x-4)] > 0 (x-4) * [(x^2)/(x-4)]

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Question 767173: Find the domain of the function.
h(x) = ln[(x^2)/(x-4)]
What I have tried on the problem so far is as follows:
[(x^2)/(x-4)] > 0
(x-4) * [(x^2)/(x-4)] > 0 * (x-4)
x^3 - 4x^2 > 0
x^2 (x-4) > 0
-(x-4) -(x-4)
x^2 > -x-4
+x +x
x^2 +x > -4
Answer by solver91311(24713) (Show Source):
You can put this solution on YOUR website!

You started out ok. The argument of the log function must be strictly greater than zero.

But consider just your numerator: . So far, we have to exclude 0.

But the denominator is positive so long as , a restriction that includes

Hence the domain is

Note the strictly greater than relationship because the value 4 itself must be excluded to avoid division by zero.

John

Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it

SOLUTION: Find the domain of the function. h(x) = ln[(x^2)/(x-4)] What I have tried on the problem so far is as follows: [(x^2)/(x-4)] > 0 (x-4) * [(x^2)/(x-4)] > 0 * (x-4) x^