Let $f(x) = 3x^2 - 4x$. Find the constant $k$ such that $f(x) = f(k - x)$ for all real numbers $x$.
+36916 f(x) = 3x^2 - 4x
f(k-x) = 3 (k-x)^2 - 4(k-x)
3 (k^2-2kx+x^2) - 4k +4x and this equals 3x^2 - 4x
3 k^2 - 6kx + 3 x^2 - 4k + 4x = 3x^2 - 4x simplify
3 k^2 - 6kx - 4k + 8x = 0
(3k -4)( k -2x) = 0
so k = 4/3 or k = 2x though I do not think this is a 'constant'
