Question

which of the following functions is the inverse of this function?
$f(x) = \frac{x + 2}{7}$

a. $p(x) = 7x - 2$

b. $q(x) = \frac{-x + 2}{7}$

c. $r(x) = \frac{7}{x + 2}$

d. $s(x) = 2x + 7$

Explanation:

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

We start with the function \( f(x)=\frac{x + 2}{7} \). Replace \( f(x) \) with \( y \), so we have \( y=\frac{x + 2}{7} \).

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

To find the inverse, we swap the roles of \( x \) and \( y \). This gives us \( x=\frac{y + 2}{7} \).

Step3: Solve for \( y \)

Multiply both sides of the equation \( x=\frac{y + 2}{7} \) by 7 to get rid of the denominator on the right side. We have \( 7x=y + 2 \). Then, subtract 2 from both sides to solve for \( y \). So, \( y = 7x-2 \).

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

We can write the inverse function as \( f^{-1}(x)=7x - 2 \), which matches the function \( p(x) \) in option A.

Answer:

A. \( p(x) = 7x - 2 \)