Find the Domain y=2^(x+9)

Problem

y=2(x+9)

Solution

1. Identify the type of function. The given equation y=2(x+9) is an exponential function of the form y=aƒ(x)

2. Determine the restrictions for exponential functions. For any exponential function with a positive base a>0 and a≠1 the domain is determined by the domain of the exponent ƒ(x)

3. Analyze the exponent. The exponent is ƒ(x)=x+9 which is a linear polynomial.

4. Evaluate the domain of the exponent. Polynomials are defined for all real numbers, meaning there are no values of x that would result in division by zero or the square root of a negative number.

5. Conclude the domain. Since the exponent is defined for all real numbers, the domain of the entire function is all real numbers.

Final Answer

Domain: *(−∞,∞)

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