Find the Domain f(x)=5/3*(4/5)^x

Problem

ƒ(x)=5/3*(4/5)x

Solution

1. Identify the type of function. The given expression is an exponential function of the form ƒ(x)=a⋅bx where a=5/3 and b=4/5

2. Analyze the restrictions for exponential functions. For any function bx where the base b is a positive constant (b>0, the exponent x can be any real number.

3. Check for denominators or radicals. There are no variables in the denominator and no square roots of negative values that would restrict the input x

4. Determine the domain. Since there are no values of x that make the expression undefined, the domain consists of all real numbers.

Final Answer

Domain: *(−∞,∞)

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