math

The function
f(x) = cx/2x+3
satisfies f(f(x))=x for all real numbers x\= -3/2. Find c.

asked by Will
  1. f(x) = cx/(2x+3)
    f(f) = cf/(2f+3) = c[cx/(2x+3)]/(2[cx/(2x+3)]+3)
    = c^2x/(2(c+3)x+9)

    So, if
    c^2x/(2(c+3)x+9) = x,
    c^2x = 2(c+3)x^2 + 9x
    2(c+3)x^2 + (9-c^2)x = 0
    x(2c+6+9-c^2) = 0
    x(15+2c-c^2) = 0
    x(5c-1)(3c+1) = 0
    So, c = 1/5 or c = -1/3

    posted by Steve

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