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

   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 

The graphs are not typed

The answer is the numbers between =5 and 5