# Thread: find image, kernel, range

1. ## 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?

2. 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.