91Ó°ÊÓ

To understand how to evaluate functions, start by substituting the specific value of the variable into the given function. For the function \( f(x) = x - 3 \), if we want to find \( f(0) \), we replace \( x \) with 0:
\[ f(0) = 0 - 3 = -3 \]
Similarly, for the function \( g(x) = x^2 - x \), if we want to find \( g(0) \), we do the same substitution:
\[ g(0) = 0^2 - 0 = 0 \]
By substituting the number directly into the function, you accurately find the value of the function at that point. This process is essential in evaluating any function, whether it is simple or complex. Always follow this substitution to avoid errors. Breaking it down step by step makes it easier to understand.

Function multiplication involves multiplying the outputs of two functions. For given functions \( f(x) \) and \( g(x) \), the product, \( (g \times f)(x) \), is obtained by multiplying their individual results for \( x \).
In our example, we first found \( f(0) = -3 \) and \( g(0) = 0 \). To find \( (g \times f)(0) \), we multiply these values:
\[ (g \times f)(0) = g(0) \times f(0) = 0 \times (-3) = 0 \]
Function multiplication is a useful tool in calculus and algebra when combining different functional relationships. It allows for understanding how multiple factors interact by observing their combined output. Always ensure to substitute and evaluate each function independently before multiplying for clarity and correctness.

Solving precalculus problems often involves combining multiple steps, including evaluating functions, function multiplication, and simplifying expressions systematically. Each step builds upon the previous one.
For the exercise provided, we operate as follows:

• First, evaluate \( f(0) \).
• Next, evaluate \( g(0) \).
• Finally, multiply the results of these evaluations.

These steps lead to the solution: \( (g \times f)(0) = 0 \).
Employing a step-by-step approach simplifies complex problems, making the solution manageable and straightforward. Breaking down the problem into smaller parts is a good strategy to solve any mathematical problem effectively. Practice with various problems helps solidify these foundational skills, ensuring you can tackle more intricate precalculus challenges in the future.