F of G stuck at distributing the 4 on the radical equation

Question

F of G(x)

f(x) = x^2 - 4x

g(x) = √x+4

pls help

Answer 1

Chad, I am not really sure on your g(x) for the square root, it could be sqrt(x) + 4 or sqrt(x+4) so i will just do in both

F(x) = x^2 - 4x

G(x) = sqrt (x)+4

(F o G)(x) means substitute all x in F(x) with G(x)

(F o G)(x) = (if g(x) = sqrt(x) + 4)

G(x)^2 - 4 x G(x) =

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

x +8sqrt(x) +16 - 4sqrt(x) - 16 =

x + 4 sqrt(x)

(F o G)(x) = (if g(x) = sqrt(x + 4)

G(x)^2 - 4 x G(x) =

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

sqrt(x +4) - 4sqrt(x+4) =