{Use of Tech} A family of superexponential functions Let ƒ(x) = (a + x)ˣ , where a > 0.




a. What is the domain of f (in terms of a)?

Verified step by step guidance

1. To determine the domain of the function \( f(x) = (a + x)^x \), we need to identify the values of \( x \) for which the expression is defined.
2. The base of the power, \( a + x \), must be positive because raising a negative number to a real power can result in a complex number, which is not within the scope of real-valued functions.
3. Therefore, we set the inequality \( a + x > 0 \) to ensure the base is positive.
4. Solving the inequality \( a + x > 0 \) gives \( x > -a \).
5. Thus, the domain of \( f(x) \) in terms of \( a \) is \( x > -a \).