Question

Suppose that the functions and are defined for all real numbers as follows. r(x)=3x^(2) s(x)=2x write the expressions for (r-s)(x) and (r+s)(x) and evaluate (r*s)(-1).

Answer 1

The expression for (r-s)(x) is found by subtracting s from r.  That difference is $3 x^{2} -2x$.  The expression for (r+s)(x) is found by adding them, which is $3 x^{2} +2x$.  Now we are told to evaluate (r*s)(x) which means they want us to multiply those and state the "new" expression that results.  $(3 x^{2} )(2x)=6x^3$.  There you go!