Question

F(X)=(X-3)^.5 G(X)=(X^2+3)^.5 find Dom(fog)x
can you help me, please ?

Answer 1

when does a square root go bad?

Answer 2

f(g) = (g-3)^.5 ; is valid for: (g-3) >= 0

g(x) = (x^2+3)^.5 ; is valid for (x^2+3) >=0

Answer 3

Dom (g) and dom f(g(X))

Answer 4

it is a dom of composition function

Answer 5

f(g) is the composition. f "is composed of" g; but the value of g is dependant upon the value of x, since g "is composed of" x.

Answer 6

therefore, the restrictions imposed on the composite f(g); is such that (g-3) >= 0; this gives you restricted values from g; to determine from the composition of g with x

Answer 7

in other words:

g-3 >= 0

g >= 3 or written in terms of x:

(x^2+3)^.5 >= 3