If f(x)=\sqrt{x-3}, what is the smallest real number x in the domain of f(f(x))?

f (f(x) )    =

√  [ √ ( x - 3) - 3 ]

Since     √ ( x - 3) - 3    must be >=  0, set this to 0

Add 3 to both sides

√ ( x - 3)    =  3       square both sides

x - 3  =  9

x =  12

So...the domain  is  [12, inf )