SOLUTION: I don't know if I understand what f(x) =.... means does the f mean function of "x" and whatever value we plug in for x results in our y value. Therefore, y can only be found rel

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Question 950516: I don't know if I understand what f(x) =.... means
does the f mean function of "x" and whatever value we plug in for x results in our y value. Therefore, y can only be found relative to the x value chosen? Assuming this is correct why isn't it the other way around why can't we compute what x is relative to y like: f(y)=x? why isn't it done this way? I don't think I understand what functions are or exactly what f(x) is actually saying.
Please help me understand thanks.
Found 2 solutions by MathLover1, addingup:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

f%28x%29 means "function of+x" and it is the classic way of writing a function
The most common name is "f", but we can have other names like "g" or “h”, or even "marmalade" if we want.
A function relates an input to an output.
Let say we have a function "f of x equals x+squared" what goes into the function is put inside parentheses () after the name of the function:
f%28x%29+shows us the function is called "f", and "x" goes in (or x is an input)
And we usually see what a function does with the input:
f%28x%29+=+x%5E2 shows us that function "f" takes "x" and squares it.
Example with f%28x%29+=+x%5E2:
an input of 4->x=4 becomes an output of 16
In fact we can write f%284%29+=+16.

Answer by addingup(3677) About Me  (Show Source):
You can put this solution on YOUR website!
A function is this thing that will take an input and chew it up and, based on what the input is, will give you a given output. Think of a sausage maker. You put the meat and herbs and spices on one end and it grinds the meat and produce a sausage at the other end.
So,a function is a special relationship where each input has a single output.
It is often written just the way you have it, "f(x)" where x is the input value. But it's not limited to x. You could have S(n) or any other symbol.
Example: f(x) = x/2 ("f of x is x divided by 2") is a function, because each input "x" has a single output "x/2". We can substitute x with values:
• f(2) = 1
• f(16) = 8
• f(−10) = −5
Example: f(x) = x^2
• f(2) = 4
• f(5) = 25
But a function has special rules:
- It must work for every possible input value
- And it has only one relationship for each input value
A more formal definition is: A function relates each element of a set
with exactly one element of another set, which can possibly the same set.
Each element means that every element in X is related to some element in Y. We say that the function covers X, which means that it relates every element of x. Note: That only applies to the elements of x. Some elements of Y might not be related to at all, and that's fine.
"...exactly one element of another set..." means that a function is single valued. It will not give back 2 or more results for the same input.
Now think back to the sausage maker. It takes all the ingredients and produces one sausage. Likewise with functions, many-to-one is allowed but one-to-many is not.
Well, I've run out of time. I hope I've helped in some small way. Don't give up part of the difficulty with math is, it's like learning a foreign language. Once you learn the vocabulary, the rest is like putting together a jigsaw puzzle, it's very mechanical. Have faith in yourself, if you don't, who will? Best of luck