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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 $x$.

 Mar 3, 2020
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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' 

             

 Mar 3, 2020

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