To determine the inverse of the function [tex]\( f(x) = \frac{x + 2}{7} \)[/tex], we need to follow these steps:
1. Express the function in terms of [tex]\( y \)[/tex]:
[tex]\[
y = \frac{x + 2}{7}
\][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] and solve for [tex]\( y \)[/tex]:
[tex]\[
x = \frac{y + 2}{7}
\][/tex]
3. Isolate [tex]\( y \)[/tex] by first eliminating the fraction:
[tex]\[
7x = y + 2
\][/tex]
4. Solve for [tex]\( y \)[/tex]:
[tex]\[
y = 7x - 2
\][/tex]
So, the inverse function [tex]\( f^{-1}(x) \)[/tex] is:
[tex]\[
f^{-1}(x) = 7x - 2
\][/tex]
Comparing this with the given options, the correct answer is:
[tex]\[
\boxed{p(x) = 7x - 2}
\][/tex]
