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Math Help - Linear transformation

  1. #1
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    Linear transformation

    φ : P4 ->R given by φ(p(x)) = p′′(0), where p′′(x) denotes the second derivative.

    Is the linear transformation injective, surjective?
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  2. #2
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    Quote Originally Posted by skittle View Post
    φ : P4 ->R given by φ(p(x)) = p′′(0), where p′′(x) denotes the second derivative.

    Is the linear transformation injective, surjective?


    Hint: \phi is injective iff \ker\phi=\{0\} , and it is surjective iff every real number

    can be written as p''(0) , for some polynomial p(x) of degree at most 4...

    Tonio
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