Question 1:
For this case we must find the inverse of the following function:
[tex]y = -3x + 8[/tex]
To do this we follow the steps below:
We exchange the variables:
[tex]x = -3y + 8[/tex]
We clear the value of the variable "y":
[tex]x-8 = -3y\\y = \frac {x-8} {- 3}\\y = \frac {8-x} {3}[/tex]
We change y for [tex]f^{-1}(x):[/tex]
[tex]f ^{-1}(x) = \frac {8-x} {3}[/tex]
ANswer:
The inverse of the given function is[tex]f ^ {-1} (x) = \frac {8-x} {3}[/tex]
Question 2:
For this case we must find the inverse of the following function:
[tex]y = \frac {3} {5} x-12[/tex]
To do this we follow the steps below:
We exchange the variables:
[tex]x = \frac {3} {5} y-12[/tex]
We clear the value of the variable "y":
[tex]x + 12 = \frac {3} {5} y\\5 (x + 12) = 3y\\5x + 60 = 3y\\y = \frac {5x} {3} + \frac {60} {3}\\y = \frac {5x} {3} +20[/tex]
We change y for[tex]f^{-1}(x)[/tex]:
[tex]f^{-1}(x) = \frac {5x} {3} +20[/tex]
ANswer:
The inverse of the given function is:[tex]f ^ {-1} (x) = \frac {5x} {3} +20[/tex]
