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๐‘“(๐‘ฅ)=2๐‘ฅ2+4๐‘ฅโˆ’5f(x)=2x 2 +4xโˆ’5๐‘”(๐‘ฅ)=6๐‘ฅ3โˆ’2๐‘ฅ2+3g(x)=6x 3 โˆ’2x 2 +3Find (๐‘“โˆ’๐‘”)(๐‘ฅ)(fโˆ’g)(x).A.(๐‘“โˆ’๐‘”)(๐‘ฅ)=6๐‘ฅ3โˆ’4๐‘ฅ2โˆ’4๐‘ฅ+8(fโˆ’g)(x)=6x 3 โˆ’4x 2 โˆ’4x+8B.(๐‘“โˆ’๐‘”)(๐‘ฅ)=โˆ’6๐‘ฅ3+4๐‘ฅ2+4๐‘ฅโˆ’8(fโˆ’g)(x)=โˆ’6x 3 +4x 2 +4xโˆ’8C.(๐‘“โˆ’๐‘”)(๐‘ฅ)=6๐‘ฅ3+4๐‘ฅโˆ’2(fโˆ’g)(x)=6x 3 +4xโˆ’2D.(๐‘“โˆ’๐‘”)(๐‘ฅ)=โˆ’6๐‘ฅ3+4๐‘ฅ2+4๐‘ฅโˆ’2(fโˆ’g)(x)=โˆ’6x 3 +4x 2 +4xโˆ’2SUBMITarrow_backPREVIOUS

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๐‘“(๐‘ฅ)=2๐‘ฅ2+4๐‘ฅโˆ’5f(x)=2x 2 +4xโˆ’5๐‘”(๐‘ฅ)=6๐‘ฅ3โˆ’2๐‘ฅ2+3g(x)=6x 3 โˆ’2x 2 +3Find (๐‘“โˆ’๐‘”)(๐‘ฅ)(fโˆ’g)(x).A.(๐‘“โˆ’๐‘”)(๐‘ฅ)=6๐‘ฅ3โˆ’4๐‘ฅ2โˆ’4๐‘ฅ+8(fโˆ’g)(x)=6x 3 โˆ’4x 2 โˆ’4x+8B.(๐‘“โˆ’๐‘”)(๐‘ฅ)=โˆ’6๐‘ฅ3+4๐‘ฅ2+4๐‘ฅโˆ’8(fโˆ’g)(x)=โˆ’6x 3 +4x 2 +4xโˆ’8C.(๐‘“โˆ’๐‘”)(๐‘ฅ)=6๐‘ฅ3+4๐‘ฅโˆ’2(fโˆ’g)(x)=6x 3 +4xโˆ’2D.(๐‘“โˆ’๐‘”)(๐‘ฅ)=โˆ’6๐‘ฅ3+4๐‘ฅ2+4๐‘ฅโˆ’2(fโˆ’g)(x)=โˆ’6x 3 +4x 2 +4xโˆ’2SUBMITarrow_backPREVIOUS

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Solution

The function (f-g)(x) is found by subtracting the function g(x) from f(x).

The function f(x) is given as 2x^2 + 4x - 5 and g(x) is given as 6x^3 - 2x^2 + 3.

So, (f-g)(x) = (2x^2 + 4x - 5) - (6x^3 - 2x^2 + 3)

This simplifies to -6x^3 + 4x^2 + 4x - 8.

So, the correct answer is B. (f-g)(x) = -6x^3 + 4x^2 + 4x - 8.

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