+0

# Domain

0
44
1

What is the smallest real number x in the domain of the function g(x) = sqrt((x - 3)^2 - (x - 18)^2)?

Feb 19, 2022

#1
+117230
+1

g(x) = sqrt((x - 3)^2 - (x - 18)^2)

$$g(x) = \sqrt{(x - 3)^2 - (x - 18)^2}\\ g(x) = \sqrt{(x^2 - 6x+9) - (x^2 -36x+ 324)}\\ g(x) = \sqrt{ - 6x+9 +36x- 324}\\ g(x) = \sqrt{ 30x- 315}\\ 30x-315\ge 0\\ 30x\ge315\\ x\ge 10.5$$

Feb 19, 2022