It is not clear whether the original function is y = [tex] \frac{x-2}{3} [/tex]
or y = x - [tex] \frac{2}{3} [/tex], so I'll provide the answer for both cases
Option 1: if the given function is:
y = [tex] \frac{x-2}{3} [/tex]
1- Swap the x and y variables:
x = [tex] \frac{y-2}{3} [/tex]
2- Isolate the y:
x = [tex] \frac{y-2}{3} [/tex]
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 - [tex] \frac{2}{3} [/tex]
1- Swap the x and y variables:
x = y - [tex] \frac{2}{3} [/tex]
2- Isolate the y:
y = x + [tex] \frac{2}{3} [/tex]
Based on the above, the inverse of the function would be:
y = x + [tex] \frac{2}{3} [/tex]
This corresponds to option D
Hope this helps :)
