Question 380268
IF we have 2 functions f(x), g(x), o is called composition of function, we have : 
(fog)(x)=f(g(x))
 

Consider f(x) = 3x+7, g(x) = x^{2}.
f o g = 3g(x)+7 = 3x^2 + 7 
 
g o f = (3x+7)^2 = 9x^2 + 42x + 49
 
This can be done in 2 steps : 

Consider f(x) = sqrt{x^2+3}, g(x) = x^2+5.
(f o g)(x) = sqrt(y^2+3), y=x^2+5=g(x), hence
= sqrt((x^2+5)^2+3) = sqrt(x^4 + 10x^2 + 28)
 
(g o f)(x) = g(y), with y=f(x)
=(y^2+5) = (f(x)^2+5) = x^2+8