Find the Domain f(x)=5(1.4)^x+2

Problem

ƒ(x)=5*(1.4)^x+2

Solution

1. Identify the type of function. The given function ƒ(x)=5*(1.4)^x+2 is an exponential function because the variable x is in the exponent.

2. Analyze the restrictions for exponential functions. Exponential functions of the form a⋅b^x+c are defined for all real numbers because any real number can be used as an exponent for a positive base.

3. Determine if there are any denominators or square roots. Since there are no divisions by zero or even roots of negative numbers, there are no values of x that must be excluded.

4. State the domain in interval notation. The domain includes all values from negative infinity to positive infinity.

Final Answer

Domain:(−∞,∞)

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