Find the Domain y=(8/3)^x

Problem

y=(8/3)x

Solution

1. Identify the type of function. The given equation y=(8/3)x is an exponential function of the form y=bx where the base b=8/3

2. Determine the restrictions on the exponent. For any exponential function with a positive base b>0 the exponent x can be any real number.

3. Evaluate the domain. Since there are no denominators containing x no square roots of negative numbers, and no logarithms, there are no values of x that make the expression undefined.

4. Express the domain in interval notation. The set of all real numbers is represented as (−∞,∞)

Final Answer

Domain: *(−∞,∞)

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