what is $(fcdot g)(x)$?\n$f(x)=x^{2}-3x$\n$g(x)=2x$\nwrite your answer as a polynomial or a rational…

Explanation:

Step1: Recall the definition of function - product

By the definition of ((f\cdot g)(x)=f(x)\cdot g(x)). Given (f(x)=x^{2}-3x) and (g(x) = 2x), we substitute these into the formula: ((f\cdot g)(x)=(x^{2}-3x)\cdot(2x)).

Step2: Use the distributive property (a(b + c)=ab+ac)

Here (a = 2x), (b=x^{2}), and (c=-3x). So ((x^{2}-3x)\cdot(2x)=x^{2}\cdot(2x)-3x\cdot(2x)).

Step3: Simplify each term using the rule (x^{m}\cdot x^{n}=x^{m + n})

For (x^{2}\cdot(2x)), since (x^{2}\cdot x=x^{2 + 1}=x^{3}), then (x^{2}\cdot(2x)=2x^{3}). For (-3x\cdot(2x)), since (x\cdot x=x^{1+1}=x^{2}), then (-3x\cdot(2x)=-6x^{2}).

Answer:

(2x^{3}-6x^{2})