To determine the interval where the value of f(g(x)) is negative, we need to analyze both functions, f and g.
Start by identifying the domain of g(x) and evaluating what values it can take. Then, plug these values into the function f. The goal is to find out where the output of f(x) is less than zero based on the range of values produced by g(x).
1. **Find the Range of g(x):** Determine what values g(x) produces over its domain. This might involve checking critical points or endpoints depending on the function’s nature.
2. **Evaluate f for those Outputs:** Next, evaluate f(y) (where y = g(x)) and find the intervals where f(y) < 0.
3. **Intersection of Intervals:** Finally, look for the intersection of the intervals defined by g(x) and where f(g(x)) is negative.
In summary, the intervals will depend significantly on the specific forms of f and g, so performing these steps methodically will guide you to the correct intervals where f(g(x)) is negative.