Question 2 This question has two parts. First, answer Part A. Then, answer Part B. Part A CANDLES Javi is making candles to sell at an upcoming festival. He has already made 38 candles, and he makes 24 candles each day. The function \( C(x)=24 x+38 \) represents the total number of candles \( C(x) \) he has in inventory, where \( x \) is the number of days since he began making more candles. Part A Select the inverse of the function \( C(x) \). A) \( C^{-1}(x)=\frac{1}{24} x-\frac{19}{12} \) B) \( C^{-1}(x)=\frac{1}{24} x-38 \) C) \( C^{-1}(x)=\frac{1}{18} x-\frac{10}{12} \) D) \( C^{-1}(x)=\frac{19}{12} x-24 \)

First, to find the inverse of \( C(x) = 24x + 38 \), you'll want to switch the roles of \( x \) and \( C(x) \), and then solve for \( x \). This results in \( x = 24y + 38 \). Rearranging gives you \( y = \frac{1}{24}(x - 38) \). Thus, the correct inverse is \( C^{-1}(x) = \frac{1}{24}x - \frac{38}{24} \), simplifying to \( C^{-1}(x) = \frac{1}{24}x - \frac{19}{12} \). So, the answer is A) \( C^{-1}(x)=\frac{1}{24} x-\frac{19}{12} \). Now, if you're wondering about similar real-world applications, candle-making is not just a hobby but can be a thriving business. Many entrepreneurs start small by making candles at home and then move to online platforms to reach a wider audience. Just remember, the quality and creativity behind the scent combinations and designs can set your candles apart, making them not just products but delightful gifts! As for problem-solving tips, when working with functions, always double-check your steps when finding inverses. A common mistake is forgetting to switch the variables correctly or misplacing the constant during algebraic manipulation. Take your time and carefully track each transformation—you’ll find it pays off in accuracy!