1Cademy - Evaluating $$(f \cdot g)(2)$$ for $$f(x) = x + 2$$ and $$g(x) = x^2 - 3x

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Multiplying $f(x) = x + 2$ and $g(x) = x^2 - 3x - 4$

Example

Evaluating $(f \cdot g)(2)$ for $f(x) = x + 2$ and $g(x) = x^2 - 3x - 4$

To evaluate the product function $(f \cdot g)(2)$ for $f(x) = x + 2$ and $g(x) = x^2 - 3x - 4$ , first determine the general product function, which is $(f \cdot g)(x) = x^3 - x^2 - 10x - 8$ . Next, substitute $x = 2$ into this resulting polynomial: $(f \cdot g)(2) = 2^3 - 2^2 - 10(2) - 8$ . Simplify the expression according to the order of operations: $8 - 4 - 20 - 8$ , which sums to $-24$ . Thus, $(f \cdot g)(2) = -24$ .