Function Notation 1

[nycmathdad]

Someone recently told me that f(x) is not a function.The person went on to say that f represents the function while f(x) represents a number. Is this true?

 

[jonah2.0]

Beer soaked ramblings follow.

Someone recently told me that f(x) is not a function.The person went on to say that f represents the function while f(x) represents a number. Is this true?

harpazo is referring to

Is g(x) Continuous?

Determine whether g(x) = (x^2 + 9)/(x^2 - 4) is continuous at x = 2. Let me try this one. Is f(2) defined? When x is 2, g(x) becomes (x^2 + 9)/0, which DNE. We can't divide by zero. Since condition 1 fails, there's no need to test conditions 2 and 3. I say, g(x) is discontinuous at x =...

mathforums.com

 

[Harry_the_cat]

Someone recently told me that f(x) is not a function.The person went on to say that f represents the function while f(x) represents a number. Is this true?

I'd disagree with that.
f(x) is a function of x. f is the "name" of the function, x is the independent variable.
Generally, f(x) takes on a value when x takes on a value.

 

[nycmathdad]

I'd disagree with that.
f(x) is a function of x. f is the "name" of the function, x is the independent variable.
Generally, f(x) takes on a value when x takes on a value.

I guess we all have a way to express certain math notations.

 

[Dr.Peterson]

Someone recently told me that f(x) is not a function.The person went on to say that f represents the function while f(x) represents a number. Is this true?

The proper, formal terminology is that f is the function and f(x) is a value of the function. But it is a common idiom to speak of "the function f(x)". See here: https://mathworld.wolfram.com/Function.html . Read the whole thing, but particularly note,

Generally speaking, the symbol

refers to the function itself, while

refers to the value taken by the function when evaluated at a point

. However, especially in more introductory texts, the notation

is commonly used to refer to the function

itself (as opposed to the value of the function evaluated at

). In this context, the argument

is considered to be a dummy variable whose presence indicates that the function

takes a single argument (as opposed to

, etc.). While this notation is deprecated by professional mathematicians, it is the more familiar one for most nonprofessionals. Therefore, unless indicated otherwise by context, the notation

is taken in this work to be a shorthand for the more rigorous

.​

So in your context, go ahead and use the common notation, but be aware that this marks you as a relative beginner (which is not a bad thing to be at some point ...). When not in Rome, you don't have to speak as the Romans do.

 

[nycmathdad]

The proper, formal terminology is that f is the function and f(x) is a value of the function. But it is a common idiom to speak of "the function f(x)". See here: https://mathworld.wolfram.com/Function.html . Read the whole thing, but particularly note,

Generally speaking, the symbol

refers to the function itself, while

refers to the value taken by the function when evaluated at a point

. However, especially in more introductory texts, the notation

is commonly used to refer to the function

itself (as opposed to the value of the function evaluated at

). In this context, the argument

is considered to be a dummy variable whose presence indicates that the function

takes a single argument (as opposed to

, etc.). While this notation is deprecated by professional mathematicians, it is the more familiar one for most nonprofessionals. Therefore, unless indicated otherwise by context, the notation

is taken in this work to be a shorthand for the more rigorous

.​

So in your context, go ahead and use the common notation, but be aware that this marks you as a relative beginner (which is not a bad thing to be at some point ...). When not in Rome, you don't have to speak as the Romans do.

In Rome, we don't have to speak as the Romans do but we better do as they say.