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 471948: Let f(x) = 3x^2 - 4x. Find the constant k such that f(x) = f(k - x) for all real numbers x.
Answer by richard1234(7193) (Show Source): You can put this solution on YOUR website!
We have

And we want this to equal 3x^2 - 4x for all real numbers x. The constant k will not change the degree of any of the polynomial terms, so we can equate like terms (in each equation, the LHS corresponds to f(k-x), the RHS corresponds to f(x).

3x^2 = 3x^2

-6kx + 4x = -4x

3k^2 - 4k = 0

The second equation implies -6k + 4 = -4 --> k = 4/3. The third equation factors to k(3k - 4) = 0 --> k = 0 or k = 4/3. The solution k = 4/3 satisfies both equations, so this is the answer.

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