How do you find f(g(x))

f[g(x)] = f(-2x + 2) = 4(-2x + 2) - 3  = -8x + 8 - 3 = -8x + 5

g[f(x)] = g(4x - 3) = -2(4x - 3) + 2 = 2(3 - 4x) + 2          [ since -(a - b) = b - a ]

g[f(x)] = -8x + 6 + 2 = -8x + 8

f(g(x)  says to put the function "g" into the function "f" and evaluate the result......so we have

f(g(x) =  4 [ -2x + 2  ] - 3   =   -8x + 8 - 3  =  -8x + 5

And g(f(x)  says to put the functon "f" into the funcction g and evaluate the result....so we have

g(f(x)  =  -2[4x - 3 ] + 2  = -8x + 6 + 2   = -8x + 8

And that's it....!!!