Given s(z)=z^(2)-11z+24 and w(z)=z-3, find (sw)(z)

Question

Given s(z)=z^(2)-11z+24 and w(z)=z-3, find (sw)(z)

(s/w)(z)=

Answer 1

Hi Hadassah J.,

I'm a little confused by your notation. Does sw stand for a convoluted function, i.e. s(w(z))? In that case, plug in the espression for w(z), z-3 , in whereever there is a "z" in the expression for s(z). That is, s(w(z)) = (z-3)^2 - 11*(z-3) + 24 . Or perhaps sw stands for s*w, in which case you multiply the two expressions:

s(z)*w(z) = (z^2 - 11z + 24)*(z-3) .

There is little ambiguity in the expression (s/w)(z), that's the ratio of the two expressions.

I should point out that another notation for convolution is f ° g(x) .

-- Cheers, -- Mr. d.

P.S. Congrats on being named for a noteworthy tree, Myrtus communis !