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

The range is going to be the y values (or the f(k)) values. The domain will be ur k values.

So the domain, when range is 25 is :
25 = k^2 + 2k + 1
k^2 + 2k + 1 - 25 = 0
k^2 + 2k - 24 = 0
(k + 6)(k - 4) = 0

k + 6 = 0
k = -6

k - 4 = 0
k = 4

so the domain for this one is 4 and -6

when the range is 64...
64 = k^2 + 2k + 1
k^2 + 2k + 1 - 64 = 0
k^2 + 2k - 63 = 0
(k + 9)(k - 7) = 0

k + 9 = 0
k = -9

k - 7 = 0
k = 7

so the domain for this one is -9 and 7

summary : the domain, when the range is (25,64) is { -9,-6,4,7}