SOLUTION: Let f(x) = 3x^2 - 4x. Find the constant k such that f(x) = f(k

SOLUTION: Let f(x) = 3x^2 - 4x. Find the constant k such that f(x) = f(k - x) for all real numbers x.

Question 1027846: Let f(x) = 3x^2 - 4x. Find the constant k such that f(x) = f(k - x) for all real numbers x.
Answer by ikleyn(52797) (Show Source): You can put this solution on YOUR website!
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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.
~~~~~~~~~~~~~~~~~~~~~~

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 = .

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