QuestionAugust 25, 2025

Evaluate the indicated function for f(x)=x^2-3 and g(x)=x-4 algebraically. (fg)(-4)=square

Evaluate the indicated function for f(x)=x^2-3 and g(x)=x-4 algebraically. (fg)(-4)=square
Evaluate the indicated function for f(x)=x^2-3 and g(x)=x-4 algebraically. (fg)(-4)=square

Solution
3.3(190 votes)

Answer

-104 Explanation 1. Define the product of functions The product (fg)(x) is defined as f(x) \cdot g(x). 2. Substitute and simplify Substitute f(x) = x^2 - 3 and g(x) = x - 4 into (fg)(x) = (x^2 - 3)(x - 4). 3. Expand the expression Expand (x^2 - 3)(x - 4) to get x^3 - 4x^2 - 3x + 12. 4. Evaluate at x = -4 Substitute x = -4 into x^3 - 4x^2 - 3x + 12: (-4)^3 - 4(-4)^2 - 3(-4) + 12 = -64 - 64 + 12 + 12 = -104.

Explanation

1. Define the product of functions<br /> The product $(fg)(x)$ is defined as $f(x) \cdot g(x)$.<br />2. Substitute and simplify<br /> Substitute $f(x) = x^2 - 3$ and $g(x) = x - 4$ into $(fg)(x) = (x^2 - 3)(x - 4)$.<br />3. Expand the expression<br /> Expand $(x^2 - 3)(x - 4)$ to get $x^3 - 4x^2 - 3x + 12$.<br />4. Evaluate at $x = -4$<br /> Substitute $x = -4$ into $x^3 - 4x^2 - 3x + 12$: <br /> $(-4)^3 - 4(-4)^2 - 3(-4) + 12 = -64 - 64 + 12 + 12 = -104$.
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