Function notation can look a heck of a lot like the distributive property.
Context is Everything
Mathematics is a language. We use it to communicate. Mathematics has symbols that
we arrange to communicate information, just like letters in the alphabet.
And, just like letters forming words, we over use them. We use the same arrangment
of letters to mean different ideas.
Example: bat
Is a bat flying around in a cave or are your trying to hit a baseball with a bat?
Same in mathematics.
Example: \(f(a + b)\)
- \(f(a + b) = f(a) + f(b)\)
- \(f(a + b) \ne f(a) + f(b)\)
It depends on what \(f\) is representing.
If \(f\) is the name of a function, then \(f(a + b) \ne f(a) + f(b)\). On the other hand, if \(f\) is the name of a variable, then this is just multiplication and we can distribute.
This issue is not going away.
You are learning a new language. You are learning a new alphabet. You are learning
new words.
You are learning to communicate with this new language about new concepts and
ideas and skills.
You are learning how to read.
It is going to take a while. But, you can’t even begin until you understand that you are reading and that the context affects the meaning of the words, just like in any language.
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more examples can be found by following this link
More Examples of Functions