Certainly! To find the inverse of the given function [tex]\( f(x) = \frac{x + 2}{7} \)[/tex], follow these steps:
1. Express the function with [tex]\( y \)[/tex] instead of [tex]\( f(x) \)[/tex]:
[tex]\[
y = \frac{x + 2}{7}
\][/tex]
2. Swap [tex]\( x \)[/tex] and [tex]\( y \)[/tex] to find the inverse function:
[tex]\[
x = \frac{y + 2}{7}
\][/tex]
3. Solve for [tex]\( y \)[/tex] to find the inverse function:
[tex]\[
x = \frac{y + 2}{7}
\][/tex]
Multiply both sides by 7 to isolate [tex]\( y + 2 \)[/tex]:
[tex]\[
7x = y + 2
\][/tex]
Subtract 2 from both sides to solve for [tex]\( y \)[/tex]:
[tex]\[
y = 7x - 2
\][/tex]
Thus, the inverse function is [tex]\( p(x) = 7x - 2 \)[/tex].
Given the options:
A. [tex]\( p(x) = 7x - 2 \)[/tex]
B. [tex]\( q(x) = \frac{-x + 2}{7} \)[/tex]
C. [tex]\( r(x) = \frac{7}{x + 2} \)[/tex]
D. [tex]\( s(x) = 2x + 7 \)[/tex]
Option A, [tex]\( p(x) = 7x - 2 \)[/tex], is the correct inverse function of [tex]\( f(x) = \frac{x + 2}{7} \)[/tex].
Therefore, the correct answer is:
A. [tex]\( p(x) = 7x - 2 \)[/tex]
