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

Learn Before

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, $(f \cdot g)(2) = -24$ .

Updated 2026-06-18

Contributors are:

Who are from:

References

OpenStax Intermediate Algebra

Learn After

A manufacturing engineer is analyzing a production line where the material cost per unit is modeled by $f(x) = x + 2$ and the volume of units produced is modeled by $g(x) = x^2 - 3x - 4$ . To find the total material cost at a production level of 2 units, the engineer evaluates $(f \cdot g)(2)$ . Arrange the following steps in the correct order to find this value by first determining the general product function.
A logistics analyst uses two mathematical models to predict warehouse performance: $f(x) = x + 2$ and $g(x) = x^2 - 3x - 4$ , where $x$ represents a seasonal adjustment factor. According to the technical specifications for these models, what is the value of the product function evaluation $(f \cdot g)(2)$ ?
A systems analyst is verifying the output of a performance model defined by the functions $f(x) = x + 2$ and $g(x) = x^2 - 3x - 4$ . True or False: According to the model specifications, evaluating the product function $(f \cdot g)(2)$ results in a final value of ${}-24$ .
A supply chain analyst is validating a performance model where transportation costs are modeled by $f(x) = x + 2$ and volume variance is modeled by $g(x) = x^2 - 3x - 4$ . According to the technical specifications for these models, match each mathematical component to its correct simplified value or form.
Maintenance Specification Review
A corporate financial analyst is reviewing two revenue forecast models, $f(x) = x + 2$ and $g(x) = x^2 - 3x - 4$ . According to the established procedure for determining the combined product forecast, the evaluated result of $(f \cdot g)(2)$ is ____.
Evaluating Combined Performance Metrics

Learn Before

Related

Learn After