Question

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Answer 1

In order to calculate the function (f/g)(x), we need to divide f(x) by g(x).

First, let's find the zeros of the function f(x), so we can write it in the factored form:

`\begin{gathered} f(x)=-10x^2+30x+40\\ \\ a=-10,b=30,c=40\\ \\ x=(-b\pm√(b^2-4ac))/(2a)\\ \\ x=(-30\pm√(900+1600))/(-20)\\ \\ x_1=(-30+50)/(-20)=-1\\ \\ x_2=(-30-50)/(-20)=4 \end{gathered}`

So the factored form is:

`\begin{gathered} f(x)=a(x-x_1)(x-x_2)\\ \\ f(x)=-10(x+1)(x-4) \end{gathered}`

Now, calculating the composite function, we have:

`(f(x))/(g(x))=(-10(x+1)(x-4))/(-5x-5)=(-10(x+1)(x-4))/(-5(x+1))=2(x-4)=2x-8`