Question

write an equation of the inverse for the one-to-one function as defined.
p(x) = x + 9
the equation of the inverse is $p^{-1}(x) = \square$.

Explanation:

Step1: Replace \( p(x) \) with \( y \)

We start with the function \( p(x) = x + 9 \). Replace \( p(x) \) with \( y \), so we have \( y = x + 9 \).

Step2: Swap \( x \) and \( y \)

To find the inverse, we swap the roles of \( x \) and \( y \). This gives us \( x = y + 9 \).

Step3: Solve for \( y \)

Now, we solve the equation \( x = y + 9 \) for \( y \). Subtract 9 from both sides of the equation: \( y = x - 9 \).

Step4: Replace \( y \) with \( p^{-1}(x) \)

Finally, we replace \( y \) with \( p^{-1}(x) \) to get the inverse function. So, \( p^{-1}(x) = x - 9 \).

Answer:

\( x - 9 \)