Finding $(f-g)(x)$ for $f(x) = 3x^2 - 5x + 7$ and $g(x) = x^2 - 4x - 3$

A logistics manager uses the function $T(x)$ to represent the total time required for a delivery route and $S(x)$ to represent the time spent on rest stops. To determine the function for active driving time, the manager must calculate the difference $(T - S)(x)$. According to the mathematical definition of subtracting functions, which of the following expressions is equivalent to $(T - S)(x)$?

A business analyst calculates a company's net profit function $(R - E)(x)$ by subtracting the total expense function $E(x)$ from the total revenue function $R(x)$. To evaluate this difference correctly, the analyst follows a specific three-step algebraic process. Arrange the following steps in the correct order to evaluate $(R - E)(x)$.

An inventory manager uses the function $S(x) = (I - D)(x)$ to calculate sellable stock, where $I(x)$ is total inventory and $D(x)$ is the number of damaged items. True or False: According to the mathematical process for subtracting functions, the manager must distribute the subtraction sign across every term within the polynomial expression for $D(x)$ to evaluate $S(x)$ correctly.

A project manager uses mathematical models to track various expenses. When calculating the difference between two functions, such as total budget and current spending, specific notations and steps must be recalled. Match each mathematical element of the function subtraction process with its correct description.

An operations manager calculates the difference between an efficiency model $E(x)$ and a waste model $W(x)$. To correctly evaluate $(E - W)(x) = E(x) - W(x)$, the manager substitutes the polynomial expressions and then must carefully distribute the ____ sign across the second polynomial before combining like terms.