For this case we must find the inverse of the following function:
[tex]f (x) = \frac {6} {5} x-3[/tex]
We change [tex]f (x)[/tex] by y:
[tex]y = \frac {6} {5} x-3[/tex]
We exchange the variables:
[tex]x = \frac {6} {5} y-3[/tex]
We clear the variable "y":
We add 3 to both sides of the equation:
[tex]x + 3 = \frac {6} {5} y[/tex]
We multiply by 5 on both sides of the equation:
[tex]5x + 15 = 6y[/tex]
We divide between 6 on both sides of the equation:
[tex]y = \frac {5x + 15} {6}[/tex]
We simplify:
[tex]y = \frac {5x} {6} + \frac {15} {6}\\y = \frac {5x} {6} + \frac {5} {2}[/tex]
We change y for[tex]f^{ - 1} (x)[/tex]:
[tex]f ^ {- 1 }(x) = \frac {5x} {6} + \frac {5} {2}[/tex]
Finally, the inverse function is:
[tex]f ^ {- 1} (x) = \frac {5x} {6} + \frac {5} {2}[/tex]
Answer:
[tex]f ^ {- 1} (x) = \frac {5x} {6} + \frac {5} {2}[/tex]
