Answers

2016-06-28T15:36:35+08:00
A. f(g(x))
    g(x) = 2x+3
    f(g(x)) = f(2x+3)
    f(2x+3) = x-4/2
    f(2x+3) = 2x +3 -4/2
    
f(2x+3) = 2x-1/2

b. g(f(x))
    fx = x-4/2
    g(f(x)) = g(x-4/2)
    
g(x-4/2) = 2x +3
    
g(x-4/2) = 2(x-4/2) +3
    
g(x-4/2) = x-4 +3 (the 2 has been canceled)
    
g(x-4/2) = x-1

c. f(g(x+1)) 
    g(x+1) = 2x+3
    
g(x+1) = 2(x+1) +3
    
g(x+1) = 2x +2 +3
    
g(x+1) = 2x +5
    f(g(x+1)) = f(2x+5)
    
f(2x+5) = x-4/2
    
f(2x+5) = 2x +5-4/2
    
f(2x+5) =  2x +1/2

d. g(f(x+1)) 
    f(x+1) = x-4/2
    
f(x+1) = x+1-4/2
    
f(x+1) = x -3/2
    g(f(x+1)) = g(x-3/2)
    
g(x-3/2) = 2x+3
    
g(x-3/2) = 2(x-3/2)+3
    
g(x-3/2) = x-3+3 (the 2 has been canceled)
    g(x-3/2) = x
0