For fx x2 4 and gx squareroot 8 x find f g x the domain

For f(x) = x^2 + 4 and g(x) = squareroot 8 - x, find (f g) (x); the domain of f g (f g) (x) = (Simplify your answer.)

Solution

f(x) = x^2 + 4

g(x) = sqrt (8-x)

(fog)(x) = plug g(x) into f(x)

= (sqrt (8-x)^2 ) + 4

= 8 - x + 4

= -x + 12

so (fog)(x) = - x + 12

domain is all values of x greater than equal to 8

interval notation of domain is [ 8 , infinity )