Problem 112 - Precalculus Essentials

Question

Does \(f(x)\) mean \(f\) times \(x\) when referring to a function \(f ?\) If not, what does \(f(x)\) mean? Provide an example with your explanation.

Step-by-Step Solution

Answer

\(f(x)\) does not mean \(f\) times \(x\). It represents a function named \(f\) applied to an input \(x\).

Step 1: Function Notation

In mathematics, \(f(x)\) represents a function. It does not mean \(f\) times \(x\). Instead, \(f(x)\) describes an operation that is being performed on \(x\) by the function \(f\). \(f\) is the name of the function, and \(x\) is the variable that the function is being applied to.

Step 2: Function Definition

A function is a process or a rule that associates each element \(x\) of a set, called the domain, to a single element \(y\) of another set, called the codomain or range.

Step 3: Function Example

For instance, consider a function \(g(x)\) that doubles the value of \(x\). So, for this function, \(g(2)\) would be \(4\), \(g(5)\) would be \(10\), and so on. The rule defined by the function is applied to the input (e.g., \(2\) or \(5\)) to generate the output (e.g., \(4\) or \(10\)).