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

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Question 1161350: The range of the function f(k) = k2 + 2k + 1 is {25, 64}. What is the function’s domain?
Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) About Me  (Show Source):
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The range of the function f%28k%29+=+k%5E2+%2B+2k+%2B+1 is { 25,64 }. What is the function’s domain?
k%5E2+%2B+2k+%2B+1+=+25
k%5E2+%2B+2k+-+24+=+0
k%5E2+%2B+2k+-+24+=+0
%28k+-+4%29+%28k+%2B+6%29+=+0
=>k=4 and k=-6
k%5E2+%2B+2k+%2B+1+=+64
k%5E2+%2B+2k+-+63+=+0
%28k+-+7%29+%28k+%2B+9%29+=+0
=>k=7 and k=-9
the domain is:{ -9, -6, 4, 7 }


Answer by ikleyn(52787) About Me  (Show Source):
You can put this solution on YOUR website!
.

The function is  

    f(k) = k%5E2+%2B+2k+%2B+1 = %28k%2B1%29%5E2.


The domain is   the union of two sets


First set is  k+1 = {5,8},    or   k = {4,7}.


Second set is k+1 = {-5,-8},  or   k = {-6,-9}.


ANSWER.  The domain is  {-9,-6,4,7}.