Domain of a function?

The following intervals contained in the domain of the function
x−3÷x2−4 lnx
are?

1 Answer
R. Nguyen
Jul 29, 2018

The domain for this function is (0,∞). If an interval I is contained in the domain of this function, it must be a subset of (0,∞) (that is, I⊆(0,∞)).

Explanation:

The most common things to look at when considering the domain of a function are:

  1. Division by 0

  2. Square root of a negative number

  3. Natural logarithm of non-positive number

Test for the restrictions and combine them to arrive at a final answer.

x−3x2−4lnx

There is division in 3x2. We must ensure that the denominator is not equal to 0.

x2≠0

⇒x≠0

There are no square roots.

There is a natural logarithm in 4lnx. We must ensure that the input is greater than 0.

x>0

Combining x≠0 and x>0, we simply have x>0.

The domain for this function is therefore (0,∞). If an interval I is contained in the domain of this function, it must be a subset of (0,∞) (that is, I⊆(0,∞)).

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