Question

Domain of a function?

The following intervals contained in the domain of the function
`x-3-:x^2-4` lnx
are?

Answer 1

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

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 - 3/x^2 - 4lnx`

There is division in `3/x^2`. We must ensure that the denominator is not equal to `0`.

`x^2 ne 0`

`=> x ne 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 ne 0` and `x > 0`, we simply have `x > 0`.

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