Find the domain of the function. \( g(x)=\frac{5}{4-3 x} \) Choose the correct domain below. A. \( \{x \mid x \) is a real number and \( x \neq 5\} \) B. \( \left\{x \mid x\right. \) is a real number and \( \left.x \geq \frac{4}{3}\right\} \) C. \( \left\{x \mid x\right. \) is a real number and \( \left.x \neq \frac{4}{3}\right\} \) D. \( \{x \mid x \) is a real number and \( x \neq 0\} \)

To find the domain of the function \( g(x) = \frac{5}{4 - 3x} \), we need to determine when the denominator is not equal to zero. Setting the denominator to zero gives us the equation \( 4 - 3x = 0 \). Solving for \( x \), we find \( x = \frac{4}{3} \). Therefore, the function is undefined at this value. The domain consists of all real numbers except \( \frac{4}{3} \). So, the correct choice is C: \( \{x \mid x \) is a real number and \( x \neq \frac{4}{3}\} \). Additionally, there's a fun twist in mathematics known as the "excluded value" concept! Just like not inviting that one friend to a party who might cause chaos – in this case, we need to exclude \( x = \frac{4}{3} \) to keep our function nice and smooth! Lastly, this exercise on finding domains is a crucial tool in calculus. Understanding when functions misbehave helps in controlling the chaos in other areas like limits and integrals! So, keep practicing; it’s all part of the grand math adventure!