What is the smallest real number in the domain of the function g(x) = sqrt((x - 3)^2 - (x - 15)^2)?
Simplify as
sqrt [ x^2 -6x + 9 - x^2 + 30x - 225 ] =
sqrt [ 24x - 216 ]
This will be smallest when the expression inside the radical = 0......so.....
24x - 216 = 0
24x = 216
x = 216 / 24 = 9
The smallest number in the domain is x = 9
