91Ó°ÊÓ

When we talk about function evaluation, we're referring to the process of finding the value of a function when certain values are substituted for the variables. In our exercise, the function given is \(f(x) = 3 - 3x\). To evaluate this function for a specific value, we follow a simple but crucial step: replace the variable \(x\) with the given number. For instance, to find \(f(3)\), we substitute \(x\) with 3, resulting in the calculation \(f(3) = 3 - 3 \times 3 = -6\).

Similarly, for \(f(0)\), we use 0 as our value of \(x\), leading to \(f(0) = 3 - 3 \times 0 = 3\), and for \(f(-1)\), we replace \(x\) with -1, giving us \(f(-1) = 3 - 3 \times (-1) = 6\). It's important to always use parentheses around the substituted numbers to avoid making errors with signs and operations.

The substitution method plays a vital role in both evaluating functions and solving equations. In the context of our problem, this method involves replacing the variable \(x\) with a specific value and computing the result. For example, to find \(f(3)\), we used substitution to make our calculation clearer and more accurate. It ensures that the operation between numbers, in this case subtraction and multiplication, is correctly applied.

We also used substitution to solve for \(x\) when \(f(x)\) is set equal to \(-3x\). By substituting \(f(x)\) with its equation \(3 - 3x\), we were able to compare terms and find that \(3 - 3x = -3x\) leads to the solution \(x = 1\). Effectively using the substitution method is key for simplifying complex problems and is an essential skill in algebra.

Solving equations often involves finding the values of variables that make the equation true. Our exercise includes a specific type of equation, a linear function in the form of \(f(x) = 3 - 3x\), equating it to \(-3x\) to find the requisite value of \(x\). Here's how we approached it:

First, we set \(3 - 3x\) equal to \(-3x\), which was our equation. Then, we looked for values of \(x\) that satisfied this equality. Upon simplification, we discovered that the equation holds for \(x = 1\), meaning that if we plug this value into the function, we would get the same result as \(-3x\). Solving equations like this helps to understand functions better and figure out their behavior based on the input values.