Question

Suppose that the functions r and s are defined for all real numbers x as follows. =rx−x5 =sx+2x3 write the expressions for ·rsx

Answer 1

Although the question's print is not clear, to the best of my knowledge, as I can see, We are given that:

$r(x)=-x^5$ and $s(x)=2x^3$

No, we know that, by definition:

$(r.s)(x)=r(x)\times s(x)$

$\therefore (r.s)(x)=-x^5\times 2x^3=-2x^8$

Thus, for the functions r and s which are defined for all real numbers x, the answer to the question asked is:

$(r.s)(x)=-2x^8$