Find the Domain f(x)=0.25(4)^x-6

Problem

ƒ(x)=0.25*(4)^x−6

Solution

1. Identify the type of function. The function ƒ(x)=0.25*(4)^x−6 is an exponential function of the form ƒ(x)=a⋅b^x+c

2. Analyze the restrictions for exponential functions. For any real number x the expression b^x is defined as long as the base b is a positive constant.

3. Determine the domain. Since there are no denominators containing x no square roots of negative numbers, and no logarithms, the variable x can be any real number.

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

Final Answer

Domain:(−∞,∞)

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