Problem

Given the functions \(f(x) = 4x + 3\) and \(g(x) = 2x^2 - 5\), find the product \((f \cdot g)(x)\).

Answer

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Answer

Finally, we expand the product to get \((f \cdot g)(x) = 8x^3 + 6x^2 - 20x - 15\).

Steps

Step 1 ：First, we write down the given functions: \(f(x) = 4x + 3\) and \(g(x) = 2x^2 - 5\).

Step 2 ：Next, we find the product of the two functions, which is \((f \cdot g)(x) = f(x) \cdot g(x)\).

Step 3 ：Substituting the given functions into the equation, we get \((f \cdot g)(x) = (4x + 3) \cdot (2x^2 - 5)\).

Step 4 ：Finally, we expand the product to get \((f \cdot g)(x) = 8x^3 + 6x^2 - 20x - 15\).

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