Questions: A one-to-one function is given. Write an equation for the inverse function. g(x) = (3-x)/8 g^-1(x) =

Solution Steps

To find the inverse of a one-to-one function, we need to swap the roles of \( x \) and \( y \) in the equation and then solve for \( y \). This will give us the equation for the inverse function.

The original function is given by

\[ g(x) = \frac{3 - x}{8} \]

To find the inverse function, we swap \( x \) and \( y \) in the equation:

\[ x = \frac{3 - y}{8} \]

Now, we solve for \( y \):

1. Multiply both sides by 8:

\[ 8x = 3 - y \]

2. Rearranging gives:

\[ y = 3 - 8x \]

Thus, the inverse function is

\[ g^{-1}(x) = 3 - 8x \]

Final Answer