Question

F^-1(4) when f(x) = 3x - 4/ 5

Answer 1

Answer:
`f^(-1)(4)=(8)/(5)`

Explanation:

1. You need to find the Inverse function
`f^(-1)(x)`:

- Given the function f(x):

`f(x) = 3x - (4)/( 5)`

- Rewrite it with
`f(x)=y`:

`y= 3x - (4)/( 5)`

- Now you must solve for "x":

`y+(4)/( 5) = 3x\\\\(y+(4)/( 5))(3)=x\\\\x=(y)/(3)+(4)/(15)`

- Now you must exchange the variables:

`y=(x)/(3)+(4)/(15)`

- Then:

`f^(-1)(x)=(x)/(3)+(4)/(15)`

2. Substitute
`x=4` into the Inverse function and then evaluate:

`f^(-1)(4)=((4))/(3)+(4)/(15)\\\\f^(-1)(4)=(8)/(5)`