Answer:
g(x)=(x+3/5)/2
Step-by-step explanation:
When f(g(x)) and (g(f(x)) both equal x, they are inverses.
f(x)=2x-3/5
y=2x-3/5
x=2y-3/5
x+3/5=2y
(x+3/5)/2=y
(x+3/5)/2=g(x)
For this case we must find the inverse of the following function:
[tex]f (x) = 2x- \frac {3} {5}[/tex]
We change f(x) by y:
[tex]y = 2x- \frac {3} {5}[/tex]
We exchange the variables:
[tex]x = 2y- \frac {3} {5}[/tex]
We cleared "y":
Adding[tex]\frac {3} {5}[/tex] to both sides of the equation:
[tex]x + \frac {3} {5} = 2y[/tex]
DIviding between 2 to both sides of the equation:
[tex]y = \frac {x} {2} + \frac {3} {10}[/tex]
We change y for[tex]f^{-1} (x)[/tex]:
[tex]f ^ {- 1} (x) = \frac {x} {2} + \frac {3} {10}[/tex]
Answer:
[tex]f ^{ - 1} (x) = \frac {x} {2} + \frac {3} {10}[/tex]
