Answer:
Second option {x | x > 7}
Step-by-step explanation:
We have the function

We know that the square root of a negative number has no solution in the real ones. Therefore the domain of this function is 
When applying the transformation:
we have a translation of the original function in 7 units to the right and 2 units to the top:

In the same way we must guarantee that 
Then
.
Therefore the domain of f(x) is {x | x > 7}
By plugging (k-2) in t, we can write that

He made an error is step 2
3x + 18 = 2x +8
subtract 2x from each side
x + 18 = 8