# What is the domain and range of f(x)= ln(x) + ln(1-x)?

##### 1 Answer

#### Explanation:

**Domain:** we need to make sure that both logarithms exist, and every logarithm has the same request: its argument must be strictly positive. So, the first term,

Again, both conditions need to be satisfied, so we must consider only the numbers between

**Range:** As for the range, it's useful to see what happens at the borders of the domain. We have

Similarly, we have

So, our function looks like an upside-down "U". The range is thus unbounded towards negative infinity. As for the maximum, we simply need to derive:

and we have

Since