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