9514 1404 393
Answer:
x = 2
Explanation:
To find g(x), we can start with the inverse of f(x).
f(y) = x . . . . . . . solve this to find f^-1(x)
3y -2 = x
3y = x +2 . . . . add 2
y = (x +2)/3 = f^-1(x) . . . . divide by 3
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Now, we can find g(x):
f^-1(f(g(x)) = g(x)
f^-1(6x -2) = ((6x -2) +2)/3 = g(x)
6x/3 = g(x) = 2x
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Now, we want g(f(x)) = 8
g(3x -2) = 8
2(3x -2) = 8
6x -4 = 8
6x = 12
x = 2 . . . . makes g(f(x)) = 8