Problem 49 - Introductory Algebra for College Students

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

No, \(f(x)\) does not mean \(f\) times \(x\). It denotes a function named \(f\) and \(x\) is the variable or input into the function. For example, for the function \(f(x) = 2x + 3\), \(f(1)\) would output 5.

Step 1: Interpretation of Function Notation

The notation \(f(x)\) when referring to a function does not mean multiplication of \(f\) and \(x\). Rather, \(f(x)\) is a way to denote a function named \(f\) and \(x\) is the variable or input into the function.

Step 2: Meaning of Function Notation

The function \(f(x)\) should be read as 'the value of \(f\) at \(x\)' or 'the output of \(f\) when \(x\) is the input'. Essentially, you input \(x\) into the function \(f\) and it will produce some output. This is different from multiplication where you multiply two quantities together.

Step 3: Example of a Function

For example, consider the function \(f(x) = 2x + 3\). Here, the function takes any input \(x\) and multiplies it by 2, then adds 3. If we input 1 into the function \(f(1)\), the output will be \(2*1+3 = 5\). This demonstrates that \(f(x)\) refers to a specific operation or set of operations, specified by \(f\), applied to the input \(x\), rather than the multiplication of two quantities \(f\) and \(x\).