dassioom Campus Student ACE ehalipass New Tab MOACT My ICEV | My Cours. bus 10 v Next Mathemailics Progress check Submit Toat Reader Toob info 10 A carpet cleaning company charges a flat fee of \( \$ 25 \) and \( \$ 0.05 \) for each square foot of carpet cleaned. This is modeled in the function below. \[ c=0.05 x+25 \] Which of the following functions is the inverse of the function above? A. \( A(c)=20 c+\frac{1}{25} \) B. \( A(c)=25 c+0.05 \) C. \( A(c)=0.05(c-25) \) D. \( A(c)=\frac{c-25}{0.05} \) Reset Next

To find the inverse of the function \( c = 0.05x + 25 \), we begin by swapping \( c \) and \( x \) and solving for \( x \). Rearranging gives us \( x - 25 = 0.05c \), and dividing both sides by \( 0.05 \) yields \( x = \frac{c - 25}{0.05} \). So, the correct inverse function is \( D. A(c)=\frac{c-25}{0.05} \). Understanding that functions can have inverses helps us in real-world scenarios where we need to reverse a calculation. For instance, if a customer tells you the total cost after carpet cleaning and you want to determine the amount of carpet cleaned, you would apply the inverse function. This practical understanding emphasizes the importance of knowing both the function and its inverse in everyday life!