To find the domain of the expression cdx, where cx = 5x^2 and dx = x^3, we first need to analyze the individual components of both cx and dx.
1. **Definition of the Components**:
- For cx = 5x^2: The expression is defined for all real numbers, since polynomial functions such as this do not have restrictions like division by zero or square roots of negative numbers. Therefore, the domain of cx is (-
∞, +
∞). - For dx = x^3: Similar to cx, this expression is also a polynomial function, meaning it is defined for all real numbers. Thus, the domain of dx is also (-
∞, +
∞).
2. **Finding the Domain of cdx**: Now, since both cx and dx are defined over the entire set of real numbers, the expression cdx can be derived by multiplying cx and dx:
cdx = (5x^2)(x^3) = 5x^{2+3} = 5x^5
3. **Domain of the Function**: The function 5x^5 is also a polynomial, which means it is defined for all real numbers.
Therefore, the domain of the expression cdx is (-
∞, +
∞).