Question

Which of the following expression is the inverse of the fuction y=x-2/3? A.Y=3x+2 B.Y=2x+3 C.Y=x-3/2 D.Y=x+2/3

Answer 1

Flip the x and y position to find the inverse function, then solve for the new y. So the original is

y = x - 2/3. The inverse will be

x = y - 2/3. Now solve for y.

y = x + 2/3, so the answer is D.

Answer 2

It is not clear whether the original function is y =
`(x-2)/(3)`
or y = x -
`(2)/(3)`, so I'll provide the answer for both cases

Option 1: if the given function is:
y =
`(x-2)/(3)`

1- Swap the x and y variables:
x =
`(y-2)/(3)`

2- Isolate the y:
x =
`(y-2)/(3)`
3x = y - 2
y = 3x + 2

Based on the above, the inverse of the given function is:
y = 3x + 2
This corresponds to option A

Option 2: If the given function is:
y = x -
`(2)/(3)`

1- Swap the x and y variables:
x = y -
`(2)/(3)`

2- Isolate the y:
y = x +
`(2)/(3)`

Based on the above, the inverse of the function would be:
y = x +
`(2)/(3)`
This corresponds to option D

Hope this helps :)