6. Directions Choose the correct answer for each row. Find the inverse f^-1(x) of the function f(x)=(1)/(4)x-8

To find the inverse of the function \( f(x) = \frac{1}{4}x - 8 \), we need to follow these steps:<br /><br />1. Replace \( f(x) \) with \( y \):<br /> \[<br /> y = \frac{1}{4}x - 8<br /> \]<br /><br />2. Swap \( x \) and \( y \) to find the inverse:<br /> \[<br /> x = \frac{1}{4}y - 8<br /> \]<br /><br />3. Solve for \( y \):<br /> - First, add 8 to both sides:<br /> \[<br /> x + 8 = \frac{1}{4}y<br /> \]<br /> - Then, multiply both sides by 4 to solve for \( y \):<br /> \[<br /> 4(x + 8) = y<br /> \]<br /> - Simplify:<br /> \[<br /> y = 4x + 32<br /> \]<br /><br />Thus, the inverse function is \( f^{-1}(x) = 4x + 32 \).