document.write( "Question 1028661: Let f(x) = x^2 - 2x. Find all real numbers x such that f(x) = f(f(x)). \n" ); document.write( "

Algebra.Com's Answer #643813 by Natolino1983(23) $\"\"$ $\"About$

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If f(f(x)) = f(x) then we need to find every the solution to f(x) = x\r
\n" ); document.write( "\n" ); document.write( "X^2 -2x = x is equivalent to x^2-2x-x = 0
\n" ); document.write( " X^2 -3x = 0
\n" ); document.write( " X(x-3) =0
\n" ); document.write( " So, solutions are x=0 or x=3.\r
\n" ); document.write( "\n" ); document.write( "1) f(f(0)) =f(0^2-2×0) =f(0) (checked)
\n" ); document.write( "2) f(f(3)) = f(3^3-2×3) = f(9-6) = f(3) (checked)
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