Given $f(x)=10-2 x$, find $f(7)$.
The problem asks for the evaluation of a given linear function at a specific point. We are given the function \(f(x) = 10 - 2x\) and we need to calculate its value when \(x = 7\), which is denoted as \(f(7)\). The function is defined for all real numbers, and the task is a straightforward substitution and arithmetic operation. We are also provided with a list of potential options: -4, 56, 3, 7.
To evaluate \(f(7)\), we substitute the value \(x = 7\) directly into the function expression \(f(x) = 10 - 2x\). This gives:
\[f(7) = 10 - 2(7)\]
Now, we perform the multiplication inside the expression, which is \(2 \times 7 = 14\). Substituting this back into the expression, we get:
\[f(7) = 10 - 14\]
Finally, calculating the subtraction results in:
\[f(7) = -4\]
Comparing our result \(f(7) = -4\) with the provided options (-4, 56, 3, 7), we can clearly see that our calculated value matches the first option. Thus, the correct value for \(f(7)\) is \(-4\).
In real-life scenarios, functions like this are used to model linear relationships. For example, if a store has a base inventory of 10 items and sells 2 items per day, the number of items remaining after \(x\) days can be modeled by \(f(x) = 10 - 2x\). Calculating \(f(7)\) tells us the number of items remaining after 7 days, which in this case would mean the inventory is depleted (the negative result signifies that we have sold more items than were in the initial inventory). Understanding how to substitute values into functions is a fundamental skill for interpreting such models.