Respuesta :

xKelvin

Answer:

[tex]\displaystyle y = \frac{1}{5}x+1[/tex]

Or:

[tex]x + 5 = 5y[/tex]

Step-by-step explanation:

We have the function:

[tex]y=5x-5[/tex]

And we want to find its inverse.

To find the inverse of a function, we:

  1. Flip x and y.
  2. And solve for y.

Hence:

[tex]x=5y-5[/tex]

Solve for y. Add:

[tex]\displaystyle x + 5 = 5y[/tex]

Divide:

[tex]\displaystyle y = \frac{x+5}{5}[/tex]

Simplify. Hence:

[tex]\displaystyle y = \frac{1}{5}x+1[/tex]

In conclusion, the inverse function is:

[tex]\displaystyle y = \frac{1}{5}x+1[/tex]

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