Question

F(x)=(3x-1)/(2) find f^(-1)(2)

Answer 1

`f^(-1) (2)=(5)/(3)`

Explanation:

To find the inverse of a function, we must replace y for x and then solve for y.

`y=(3x-1)/(2) \\x=(3y-1)/(2) \\2x=3y-1\\3y=2x+1\\y=(2x+1)/(3) \\f^(-1) (x)=(2x+1)/(3)`

Now we can substitute x=2 into our inverse function

`f^(-1) (2)=(2(2)+1)/(3) \\f^(-1) (2)=(5)/(3)`