HELP functions

Question

given that f(x)=x^2-2x+2 and g(x)=√5+2x

 

(g-f)(x), (f/g)(x), domain of (f/g), the domain of (g)

 

How in the world do I do these???

Answer 1

g(f(x)) = g(x^2 - 2x + 2) = (2(x^2 - 2x +2) +5)^.5 = (2x^2 - 4x + 9)^.5

 

f(g(x)) = f((2x + 5)^.5) = [(2x + 5)^.5]^2 - 2(2x + 5)^.5 +2 = 2x + 7 - 2(2x + 5)^.5

 

The domain of g would be any x value that satisfies the inequality 2x + 5 >= 0. For this equation, the answer would x >= -2.5. Therefore for the domain of g, x >= -2.5