domain of composition of functions

Question

let f={(-2,1), (0,4) (1,2) (4,5)} and g(x)=sqr(x-3). 

Determine the domain of the composition of f and g.

Answer 1

f

-2--------> 1

 0 -------> 4

 1 --------> 2

 4 --------> 5

 

g(x) = (x-3)²

g(x) =√(x-3)

 

sqr could mean square of OR squared root. No clear indication from you! ASSUME THE SECOND VERSION.

 

f⁰g(x) = f[g(x)]  g(x) exists for x = or above 3   {3, 4, 19}

g⁰f(x) = g[f(x)]  f(x) exists for x in domain {-2, 0, 1, 4}

 

dom f[g(x)] is {3, 4, 19}

dom g[f(x)] is {0, 4}