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Alla [95]
1 year ago
10

Help 4567778776655555

Mathematics
1 answer:
zepelin [54]1 year ago
8 0

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=\frac{-b\pm\sqrt{b^2-4ac}}{2a}\\ \\ x=\frac{-30\pm\sqrt{900+1600}}{-20}\\ \\ x_1=\frac{-30+50}{-20}=-1\\ \\ x_2=\frac{-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:

\frac{f(x)}{g(x)}=\frac{-10(x+1)(x-4)}{-5x-5}=\frac{-10(x+1)(x-4)}{-5(x+1)}=2(x-4)=2x-8

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