Respuesta :

Answer:

[tex] \frac{x - 2}{7} [/tex]

Step-by-step explanation:

[tex]f(x) = 7x + 2[/tex]

[tex]let \: \: f(x) = y[/tex]

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

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

[tex]x = \frac{y - 2}{7} [/tex]

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

Answer ↓

[tex]\large\text{view\:explanation\:for\:more\:details}[/tex]

Calculations ↓

Remember , inverse functions do the opposite things in the opposite order.

Here's what happened to x here :

  1. First , it's been multiplied by 7 .
  2. Then , 2 has been added to it .

We can easily find the inverse of any function by following these steps :

  1. Set the function equal to y as follows :

f(x)=7x+2

y=7x+2

        2. Now , switch y and x places :

x=7y+2

            3. Solve for y .

First , subtract 2 on both sides :

x-2=7y

Divide by 7 on both sides :

[tex]\text{y=$\displaystyle\frac{x-2}{7}$}}[/tex]

We've found the inverse function of f(x)=7x+2.

[tex]\tiny\text{hope\:helpful}[/tex]

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