Question

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

Answer 1

if the range is{25,64}
it means. F(K) =25,64 for some value of k
for 25
25=k²+2k+1
k²+2k-24=0
k²+6k-4k-24=0
K(k+6)-4(k+6)=0
(k-4)(k+6)=0
k=-6,+4

for 64
k²+2k-63=0
k²+9k-7k-63=0
k(k+9)-7(k+9)=0
(k-7)(k+9)=0
k=-9,+7
so the domain of F(k)={ -9 , -6 , 4 , 7 }