Find the Domain x^3+3^x=64

Problem

x3+3=64

Solution

1. Identify the types of functions present in the equation. The expression x3 is a polynomial (specifically a cubic) and 3 is an exponential function.

2. Determine the domain of each individual component. Polynomial functions are defined for all real numbers, so the domain of x3 is (−∞,∞)

3. Determine the domain of the exponential component. Exponential functions with a positive base, such as 3 are also defined for all real numbers, so its domain is (−∞,∞)

4. Find the intersection of the domains. Since both functions are defined for all real values of x the sum x3+3 is defined for all real numbers.

5. Conclude that there are no restrictions such as denominators being zero or negative values inside square roots or logarithms.

Final Answer

Domain=(−∞,∞)

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