The function's domain are all of the "x" values or "k" values in this case that will satisfy the function's range. Hence, you should solve for k after that to get the function's domain after substituting for the function's range.
Now if you understand the definition of range and domain it will be a lot simpler to answer. Domain: The values that you can put into a function Range: The values that the function spits out.
So the range here is from 25 to 64. f(k)=k^2+2k+1, where f(k) is the range and k is the domain. You will have to solve two equations for the boundary values, that is: 25=k^2+2k+1 and 64=k^2+2k+1
