f(x) = 2x - 3
f(g(x)) = 21 - (3x)/(x-5)
2(g(x)) - 3 = 21 - (3x)/(x-5)
2(g(x)) = 24 - (3x)/(x-5)
g(x) = 12 - (3x/2)/(x-5)
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f(g(x)) = 2 ( 12 - (3x/2)/(x-5) ) -3
f(g(x)) = 24 - (3x)/(x-5) -3
f(g(x)) = 21 - (3x)/(x-5)
Yes, g(x) = 12 - (3x/2)/(x-5)
You can also write it as g(x) = 12 - (3x)/2(x-5)