To find the domain of the product cdx, we need to first understand the individual functions cx and dx.
1. **Determine cx:** Given that cx = 5x^2, this is a polynomial function. Polynomial functions are defined for all real numbers. Therefore, the domain of cx is:
Domain of cx: All real numbers (−∞, ∞).
2. **Determine dx:** The function dx = x^3 is also a polynomial. Similar to cx, polynomial functions are defined for all real numbers. Thus, the domain of dx is:
Domain of dx: All real numbers (−∞, ∞).
3. **Find the domain of cdx:** Since both functions cx and dx are defined for all real numbers, when we multiply them to get cdx = (5x^2)(x^3) = 5x^5, the resulting function is also a polynomial. Hence, the domain of cdx is also:
Domain of cdx: All real numbers (−∞, ∞).
In conclusion, the domain of cdx is all real numbers since both cx and dx are defined for every real number.