# Range of #log_0.5(3x-x^2-2)# ?

##### 1 Answer

#### Explanation:

Given

To understand the range, we need to find the domain.

The restriction on the domain is that argument of a logarithm must be greater than 0; this compels us to find the zeros of the quadratic:

This means that the domain is

For the range, we set the given expression equal to y:

Convert the base to the natural logarithm:

To find the minimum, compute the first derivative:

Set the first derivative equal to 0 and solve for x:

The minimum occurs at

The minimum is 2.

Because