please help me Which of the following is the inverse of the function given below?

Accepted Solution

The function is described by the rule [tex]f(x)= \frac{x+2}{7} [/tex].

The inverse function [tex]f^{-1}[/tex] is such that [tex]f(f^{-1}(x))=x[/tex].

Thus, since [tex]f(x)= \frac{x+2}{7} [/tex], we have [tex]f(f^{-1}(x))=\frac{f^{-1}(x)+2}{7}[/tex].

Equating the two ways we expressed [tex]f(f^{-1}(x))[/tex], we have:

[tex]\displaystyle{ \frac{f^{-1}(x)+2}{7}=x[/tex].

Rearranging, we have: 

 [tex]\displaystyle{ f^{-1}(x)= 7x-2[/tex].

Answer: first choice: p(x)=7x-2