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

A. {5,8}

B. {-5, - 8}

C. {3, 8}

D. {4, 7}

E. {4, 8}

k^2 + 2k + 1 = 25

k^2 + 2k + 1 - 25 = 0

k^2 + 2k - 24 = 0

(k - 4) (k + 6) = 0

k - 4 = 0; k = 4

k + 6 = 0; k = - 6

k^2 + 2k + 1 = 64

k^2 + 2k + 1 - 64 = 0

k^2 + 2k - 63 = 0

(k - 7) (k + 9) = 0

k - 7 = 0; k = 7

k + 9 = 0; k = - 9

x = - 9, - 6, 4, 7

answer

D. {4, 7}