Let f(x), g(x), and h(x) be functions satisfying the following: The y-intercept of h(x) is (0,2), g(x) satisfies g(x) = 5 for all x < 1, and the graph of f(x) passes through the point (1,6). If F(x) is the function F(x) = 2f(x) + g(h(1 x)), compute F(1).