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:
- Flip x and y.
- 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]
