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

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


   

Question 835733: Let f(x) = 3x^2 - 4x. Find the constant k such that f(x) = f(k - x) for all real numbers x.
Answer by reviewermath(1029) About Me  (Show Source):
You can put this solution on YOUR website!
Q:
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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A:
f(x) = f(k - x)
3x%5E2+-+4x = 3%28k+-+x%29%5E2+-+4%28k+-+x%29
3x%5E2+-+4x = 3%28k%5E2+-+2kx+%2B+x%5E2%29+-+4k+%2B+4x
3x%5E2+-+4x = 3x%5E2+%2B%284+-+6k%29x+%2B+%283k%5E2+-+4k%29
Therefore, 4 - 6k = -4
k = highlight%284%2F3%29