Question

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}

Answer 1

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}