Question

The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain?

Answer 1

   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.

Answer 2

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