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f(x)=4x 2 +5xโˆ’3๐‘”(๐‘ฅ)=4๐‘ฅ3โˆ’3๐‘ฅ2+5g(x)=4x 3 โˆ’3x 2 +5Find (๐‘“+๐‘”)(๐‘ฅ)(f+g)(x).A.(๐‘“+๐‘”)(๐‘ฅ)=4๐‘ฅ3+๐‘ฅ2+5๐‘ฅ+2(f+g)(x)=4x 3 +x 2 +5x+2B.(๐‘“+๐‘”)(๐‘ฅ)=4๐‘ฅ3+4๐‘ฅ2+2๐‘ฅ+2(f+g)(x)=4x 3 +4x 2 +2x+2C.(๐‘“+๐‘”)(๐‘ฅ)=โˆ’4๐‘ฅ3+7๐‘ฅ2+5๐‘ฅโˆ’8(f+g)(x)=โˆ’4x 3 +7x 2 +5xโˆ’8D.(๐‘“+๐‘”)(๐‘ฅ)=8๐‘ฅ3+2๐‘ฅ+2(f+g)(x)=8x 3 +2x+2SUBMITarrow_backPREVIOUS

Question

f(x)=4x 2 +5xโˆ’3๐‘”(๐‘ฅ)=4๐‘ฅ3โˆ’3๐‘ฅ2+5g(x)=4x 3 โˆ’3x 2 +5Find (๐‘“+๐‘”)(๐‘ฅ)(f+g)(x).A.(๐‘“+๐‘”)(๐‘ฅ)=4๐‘ฅ3+๐‘ฅ2+5๐‘ฅ+2(f+g)(x)=4x 3 +x 2 +5x+2B.(๐‘“+๐‘”)(๐‘ฅ)=4๐‘ฅ3+4๐‘ฅ2+2๐‘ฅ+2(f+g)(x)=4x 3 +4x 2 +2x+2C.(๐‘“+๐‘”)(๐‘ฅ)=โˆ’4๐‘ฅ3+7๐‘ฅ2+5๐‘ฅโˆ’8(f+g)(x)=โˆ’4x 3 +7x 2 +5xโˆ’8D.(๐‘“+๐‘”)(๐‘ฅ)=8๐‘ฅ3+2๐‘ฅ+2(f+g)(x)=8x 3 +2x+2SUBMITarrow_backPREVIOUS

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Solution

To find the sum of the functions f(x) and g(x), we simply add the corresponding terms of each function together.

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

Adding these together, we get:

(4x^3 - 3x^2 + 5) + (4x^2 + 5x - 3)

This simplifies to:

4x^3 + (4x^2 - 3x^2) + 5x + (5 - 3)

Which further simplifies to:

4x^3 + x^2 + 5x + 2

So, the sum of the functions f(x) and g(x), denoted as (f+g)(x), is 4x^3 + x^2 + 5x + 2.

Therefore, the correct answer is A. (f+g)(x) = 4x^3 + x^2 + 5x + 2.

This problem has been solved

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