What is the domain of \( f(x)=5^{x}-7 \) ? \( \{x \mid x>-7\} \) \( \{x \mid x<-7\} \) \( \{x \mid x>0\} \) \( \{x \mid x \) is a real number \( \} \)

To find the domain of the function \( f(x) = 5^x - 7 \), we need to determine the values of \( x \) for which the function is defined. 1. The term \( 5^x \) is an exponential function. Exponential functions are defined for all real numbers. Therefore, \( 5^x \) can take any real number as input. 2. Since \( 5^x \) is defined for all real numbers, the expression \( 5^x - 7 \) is also defined for all real numbers. Thus, the domain of \( f(x) = 5^x - 7 \) is: \[ \{x \mid x \text{ is a real number}\} \] This means the correct answer is: \(\{x \mid x \text{ is a real number} \}\)