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๐‘“(๐‘ฅ)=๐‘ฅ+4f(x)=x+4๐‘”(๐‘ฅ)=3๐‘ฅ2โˆ’7g(x)=3x 2 โˆ’7Find (๐‘“โ‹…๐‘”)(๐‘ฅ)(fโ‹…g)(x).A.(๐‘“โ‹…๐‘”)(๐‘ฅ)=3๐‘ฅ3+12๐‘ฅ2โˆ’7๐‘ฅโˆ’28(fโ‹…g)(x)=3x 3 +12x 2 โˆ’7xโˆ’28B.(๐‘“โ‹…๐‘”)(๐‘ฅ)=3๐‘ฅ3+28(fโ‹…g)(x)=3x 3 +28C.(๐‘“โ‹…๐‘”)(๐‘ฅ)=3๐‘ฅ3โˆ’28(fโ‹…g)(x)=3x 3 โˆ’28D.(๐‘“โ‹…๐‘”)(๐‘ฅ)=3๐‘ฅ3+12๐‘ฅ2+7๐‘ฅ+28(fโ‹…g)(x)=3x 3 +12x 2 +7x+28SUBMITarrow_backPREVIOUS

Question

๐‘“(๐‘ฅ)=๐‘ฅ+4f(x)=x+4๐‘”(๐‘ฅ)=3๐‘ฅ2โˆ’7g(x)=3x 2 โˆ’7Find (๐‘“โ‹…๐‘”)(๐‘ฅ)(fโ‹…g)(x).A.(๐‘“โ‹…๐‘”)(๐‘ฅ)=3๐‘ฅ3+12๐‘ฅ2โˆ’7๐‘ฅโˆ’28(fโ‹…g)(x)=3x 3 +12x 2 โˆ’7xโˆ’28B.(๐‘“โ‹…๐‘”)(๐‘ฅ)=3๐‘ฅ3+28(fโ‹…g)(x)=3x 3 +28C.(๐‘“โ‹…๐‘”)(๐‘ฅ)=3๐‘ฅ3โˆ’28(fโ‹…g)(x)=3x 3 โˆ’28D.(๐‘“โ‹…๐‘”)(๐‘ฅ)=3๐‘ฅ3+12๐‘ฅ2+7๐‘ฅ+28(fโ‹…g)(x)=3x 3 +12x 2 +7x+28SUBMITarrow_backPREVIOUS

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Solution

The function (fโ‹…g)(x) is found by multiplying the functions f(x) and g(x) together.

f(x) = x + 4 g(x) = 3x^2 - 7

So, (fโ‹…g)(x) = (x + 4)(3x^2 - 7)

Expanding this gives:

(fโ‹…g)(x) = 3x^3 + 12x^2 - 7x - 28

So, the correct answer is A. (fโ‹…g)(x) = 3x^3 + 12x^2 - 7x - 28.

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