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What is the f(x) notation?

Hi,

I would appreciate it if someone could explain what the significance and use of the 'f of x' notation is, particularly in graphs?
Is it just an alternative way of writing 'y' in e.g. y=2x+9?

Thanks

Reply 1

edothero

Original post by AKRYL

f(x)

means 'function of x'

You are correct in saying that an alternative of

y=2x+9\

f(x)=2x+9

you can use anything;

g(x),\ h(x)

etc

(edited 8 years ago)

Reply 2

AKRYL

Original post by edothero

f(x)

means 'function of x'

You are correct in saying that an alternative of

y=2x+9\

f(x)=2x+9

you can use anything;

g(x), \ h(x)

\

etc

Can you elaborate on what you mean by 'function of x'?

Reply 3

Zacken

Original post by AKRYL

Yeah, pretty much, f of x means function of x as someone else said previously.

It means that your rule that maps

x \mapsto 2x+9

is a function/rule that sends your

x

value to another value using a certain rule.

With this, you can then see that

f(x) = 2x + a

is a function of

x

and so

a

is a constant, or other such subtleties.

Reply 4

edothero

Original post by AKRYL

Can you elaborate on what you mean by 'function of x'?

f(x)=2x+9

f(x)

essentially means, when

x

goes in,

f(x)

comes out

Its a function with a set 'criteria' if you'd like.

For this particular function:

x \rightarrow 2x \rightarrow (2x+9)

As input

x

goes in, it gets multiplied by 2, followed by an addition of 9, then outputs

f(x)

So when

x=5

(5) \rightarrow 2(5) \rightarrow [2(5)+9]

f(x)=19

Like I said before, this could easy be

g(x)

which again represents 'g is a function of x'
Don't be thrown off by the

f

(edited 8 years ago)

Reply 5

AKRYL

Original post by Zacken

Yeah, pretty much, f of x means function of x as someone else said previously.

It means that your rule that maps

x \mapsto 2x+9

is a function/rule that sends your

x

value to another value using a certain rule.

With this, you can then see that

f(x) = 2x + a

is a function of

x

and so

a

is a constant, or other such subtleties.

So is '2x+9' the rule that is applied to the value contained within the brackets of f(x) in order to give you the value of y?

Reply 6

AKRYL

Original post by edothero

f(x)=2x+9

f(x)

essentially means, when

x

goes in,

f(x)

comes out

Its a function with a set 'criteria' if you'd like.

For this particular function:

x \rightarrow 2x \rightarrow (2x+9)

As input

x

goes in, it gets multiplied by 2, followed by an addition of 9, then outputs

f(x)

So when

x=5

(5) \rightarrow 2(5) \rightarrow [2(5)+9]

f(x)=19

Like I said before, this could easy be

g(x)

which again represents 'g is a function of x'
Don't be thrown off by the

f

So is '2x+9' the rule or set of instructions that is applied to the value contained within the brackets of f(x) ,in order to give you the value of y?

Reply 7

edothero

Original post by AKRYL

So is '2x+9' the rule that is applied to the value contained within the brackets of f(x) in order to give you the value of y?

Yes, that is correct

The

2x+9

is applied to the input.

So for example

f(2) = 2(2)+9

\therefore f(2) = 13

y = 13

So you would know that when

x=2

y=13

And you can plot that easily.

(edited 8 years ago)

Reply 8

newfanta123

Original post by AKRYL

f(x) notation essentially shows the input value for x (or whatever letter chosen to represent the variable of the equation)
E.g.
y=x+69
f(-4)=-4+69-->when x=-4, y=65

Reply 9

AKRYL

Original post by edothero

Yes, that is correct

The

2x+9

is applied to the input.

So for example

f(2) = 2(2)+9

\therefore f(2) = 13

y = 13

Ok, but what does the 'f' part of 'f(x)' represent?
Also, why is that when you write the equation of a curve, using this notation, you have to write the part highlighted in bold y=f(x)=2x+3 and not simply f(x)=2x+3?

(edited 8 years ago)

Reply 10

edothero

Original post by AKRYL

Ok, but what does the 'f' part of 'f(x)' represent?
Also, why is that when you write the equation of a curve, using this notation, you have to write the part highlighted in bold y=f(x)=2x+3?

Nothing important , its just a way of labeling the function.

You could do

f(x) = 2x+9

g(x) = 2x+9

h(x) = 2x+9

It all means the same thing.

(edited 8 years ago)

Reply 11

username738914

Original post by AKRYL

The function. What everyone else has been trying to explain.

The

f(x)

is just the name of the function you could use any letter instead of f to indicate a different function, where you have two. So

f(x) = 3x^2

and

g(x) = 2x-1

Reply 12

metaltron

Original post by AKRYL

To clarify further, f is the function and we write f(x) to be the value of the function at x. So technically f(x) isn't the function it's the value of the output of the function when the input is x.