Respuesta :

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

Answer:

Option A.

Step-by-step explanation:

The given function is

[tex]f(x)=\dfrac{x+2}{7}[/tex]

Step 1: Substitute f(x)=y.

[tex]y=\dfrac{x+2}{7}[/tex]

Step 2: Interchange x and y.

[tex]x=\dfrac{y+2}{7}[/tex]

Step 3: Isolate y.

[tex]7x=y+2[/tex]

[tex]7x-2=y[/tex]

Step 4: Substitute [tex]y=f^{-1}(x)[/tex]

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

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

The inverse of the given function is [tex]p=7x-2[/tex].

Therefore, the correct option is A.

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