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Chapter 2: Problem 112

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.

Short Answer

Expert verified
No, the notation \(f(x)\) does not mean \(f\) times \(x\). It rather signifies that \(f\) is a function of the variable \(x\), where \(f\) takes \(x\) as input and yields some output. An example could be \(f(x) = x^2\), where \(f(x)\) means squaring the input \(x\), not \(f\) multiplied by \(x\).

Step by step solution

01

Understanding function notation

Firstly, you have to understand the notation \(f(x)\). This notation does not mean that \(f\) is being multiplied by \(x\). Instead, it indicates that \(f\) is a function of \(x\). The function \(f\) takes \(x\) as input and provides some output.
02

Example Illustration of function notation

For instance, consider the function \(f(x) = x^2\). Here \(f(x)\) represents squaring the input \(x\). If you plug in 2 for \(x\), output will be \(f(2) = 2^2 = 4\). Note that \(f(2)\) does not mean \(f\) times 2, but rather it represents the function \(f\) applied to the value of 2.

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