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Math Help - find image, kernel, range

  1. #1
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    Question find image, kernel, range

    Let D2 be the operation of taking the second derivative. Find the image of 2x^2+3x^2-5x+4 under D2. Prove that D2 is a linear operator on Pn. Determing the kernel and range of D2.

    D2=10......now where?
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  2. #2
    Senior Member Shanks's Avatar
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    D is linear operator,since
    D(f+g)=D(f)+D(g) and D(kf)=kD(f) for any f,g \in P_n, k \in R.
    D(f)=0 if and only if f \in P_2.
    D(Pn)= P_{n-2} if n is greater than 2.
    Last edited by Shanks; December 6th 2009 at 06:15 PM.
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