If $f(x)=\sqrt{x-3}$, what is the smallest real number $x$ in the domain of $f(f(x))$?
ignore the dollar signs those are for LateX.
f (f(x) ) =
sqrt [ sqrt (x - 3) - 3 ]
sqrt (x - 3) - 3 must be ≥ 0
So...
sqrt ( x - 3) - 3 ≥ 0
sqrt (x - 3) ≥ 3 square both sides
x - 3 ≥ 9
x ≥ 12
So.....12 is the smallest real number in the domain
