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3 Answers

f(x)=x+2   g(x)=4x2-10
Find (FoG)(x) and (GoF)(x)
 
The notation (fog)(x) refers to a composite function.  Basically, you just replace the x in f(x) with g(x)
 
(fog)(x) = (4x2-10)+2 = 4x2-8                 Replace the x+2 with g(x)+2
 
(gof)(x) = 4(x+2)2-10 = 4x2+16x+6        Replace the x in 4x2-10 with with 4(f(x))2-10
To solve (FoG)(x), everywhere you see the value x in the function f(x) substitute the value of g(x) [in this case, 4x2-10], so in this case:
 
(FoG)(x) = (4x2-10)+2
             =   4x2-10+2
             =   4x2-8
 
Likewise, to solve (GoF)(x), everywhere you see the value x in the function g(x) substitute the value of f(x) [in this case, x+2], so in this case:

(GoF)(x) = 4(x+2)2-10
             = 4(x2+4x+4)-10
             = 4x2+16x+6
(f o g)(x)=f(g(x))
             = f(4x^2-10)
             = (4x^2 - 10) + 2 
             = 4x^2 -8
 
(g o f)(x) = g(f(x))
              = g(x+2)
              = 4(x+2)^2 - 10
              = 4(x^2+4x+4) - 10
              = 4x^2 + 16x + 16 - 10
              = 4x^2 + 16x + 6