Find the domain of the function. \( g(x)=\frac{1}{9-8 x} \) A. \( \left\{x \mid x\right. \) is a real number and \( \left.x=\frac{9}{8}\right\} \) B. \( \{x \mid x \) is a real number and \( x \neq 0\} \) C. \( \{x \mid x \) is a real number and \( x=1\} \) D. \( \left\{x \mid x\right. \) is a real number and \( \left.x=\frac{9}{8}\right\} \)

To find the domain of the function \( g(x) = \frac{1}{9 - 8x} \), we must identify when the denominator is not equal to zero since division by zero is undefined. Setting the denominator to zero gives us: \[ 9 - 8x = 0 \] \[ 8x = 9 \] \[ x = \frac{9}{8} \] Therefore, \( x \) cannot be \( \frac{9}{8} \). The domain of the function is all real numbers except \( \frac{9}{8} \). So the correct choice is: A. \( \{x \mid x \) is a real number and \( x \neq \frac{9}{8}\} \) To further explore this topic, it's interesting to note that functions with rational expressions often have specific restrictions on their domains. While it's easy to divide by most numbers, it's crucial to avoid those pesky points where the denominator equals zero—your mathematical "danger zones!" Additionally, when encountering similar functions, a helpful tip is to always set the denominator equal to zero to pinpoint those exclusion points. Avoiding mistakes is key: double-check that you’re not overlooking any potential values that might throw a wrench in your calculations!