If you would like to solve for f(g(x)) when x = 1, you can do this using the following steps:
f(x) = x^2 - 3x + 6
g(x) = x - 3/2
f(g(x)) = f(x - 3/2) = (x - 3/2)^2 - 3 * (x - 3/2) + 6
x = 1
f(g(1)) = f(1 - 3/2) = f(-1/2) = (-1/2)^2 - 3 * (-1/2) + 6 = 1/4 + 3/2 + 6 = 1/4 + 6/4 + 24/4 = 31/4 = 7 3/4
The correct result would be 7 3/4.
