For this case we have the following function:
[tex]f (x) = 4 (3x-5)[/tex]
We find the inverse of the function f - 1 (x):
We change[tex]f (x)[/tex] by y:
[tex]y = 4 (3x-5)[/tex]
We exchange the variables:
[tex]x = 4 (3y-5)[/tex]
We cleared "y":
[tex]3y-5 = \frac {x} {4}[/tex]
We add 5 to both sides:
[tex]3y = \frac {x} {4} +5[/tex]
We divide between 3 on both sides:
[tex]y = \frac {x} {12} + \frac {5} {3}[/tex]
We change y for [tex]f^{-1}(x)[/tex]:
[tex]f ^{-1}(x) = \frac {x} {12} + \frac {5} {3}[/tex]
Answer:
[tex]f ^{-1}(x) = \frac {x} {12} + \frac {5} {3}[/tex]
