Final answer:
The value of b in the function h(x) = -50/x - b is 0.
Step-by-step explanation:
To determine the value of b in the function h(x) = -50/x - b, we can substitute the given value of h at x = 1/4. The given value is -200, so we have -200 = -50/(1/4) - b. Simplifying this equation, we get -200 = -200 - b. Solving for b, we find that b = 0.