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Given f(x)=2x−7 and g(x)=3x+4, find f(x)×g(x).

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Answer:

f(x) × g(x) is equal to 6x^2 - 13x - 28

Explanation:

Given functions:

f(x) = 2x - 7

g(x) = 3x + 4

To find f(x) × g(x), we'll multiply the two functions together.

Step 1: Write down the functions to be multiplied:

f(x) × g(x) = (2x - 7) × (3x + 4)

Step 2: Apply the distributive property to multiply the terms:

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

Step 3: Multiply the first term of f(x) with each term in g(x):

2x × 3x = 6x^2

2x × 4 = 8x

The first term of f(x) has been multiplied with each term in g(x), resulting in 6x^2 and 8x, respectively.

Step 4: Multiply the second term of f(x) with each term in g(x):

-7 × 3x = -21x

-7 × 4 = -28

The second term of f(x) has been multiplied with each term in g(x), resulting in -21x and -28, respectively.

Step 5: Combine the like terms obtained from the multiplication:

f(x) × g(x) = 6x^2 + 8x - 21x - 28

The like terms, 8x and -21x, can be combined to get -13x.

Step 6: Simplify the expression:

f(x) × g(x) = 6x^2 - 13x - 28

The final result is 6x^2 - 13x - 28, which is the product of the two functions f(x) and g(x).

Therefore, f(x) × g(x) is equal to 6x^2 - 13x - 28.

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