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Function f and g are defined by
f:x→4-x and g:x→px^2+q where p and q are constants.Given that the composite function gf:x→x^2-8x+11,find
the values of p and q.

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asked by mandy
  1. f(x) = 4-x
    g(x) = px^2 + q

    g(f(x))
    = g(4-x)
    = p(4-x)^2 + q
    = p(16 - 8x + x^2) + q
    = px^2 - 8p x + 16p+q

    if px^2 - 8p x + 16p+q = x^2 - 8x + 11

    then p = 1
    16p+q = 11
    16 + q = 11
    q = -5

    and -8p = -8
    p = 1, which checks out

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    posted by Reiny

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