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Let f(x) = 3x^2 - 4x. Find the constant k such that f(x) = f(k - x) for all real numbers x.
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The condition requires that this identity would hold for all real numbers x:
= .
Simplify it step by step
= ,
= .
It would be identically zero if
= (1) and
= (2)
are hold simultaneously.
Fortunately, k = satisfies both (1) and (2).
Answer. k = .
