Why Do We Use fg(x) Instead of f(g(x))?

[adjacent]

f(x)=2x+1
g(x)=x+1

→ f(6)=2(6)+1 = 13

Why do we use fg(x) but not f(g(x)),if it follows the same way as →?

 

[Number Nine]

Uh, what? Can you please clarify your question?

 

[adjacent]

Ok.
Find:
$fg(x)$ - I put $g(x)$ in f.That is,$2(g(x))+1$

But when it comes for $f(2)$ for example,I put the thing in the bracket on f - 2(2)+1
Why do we write $fg(x)$ but not $f(g(x))$ because I have to put $g(x)$ in the function f?

 

[Mark44]

The notation fg normally means the product of f and g, not their composition.

(fg)(x) $\equiv$ f(x) * g(x)

When someone writes f(g(x)), they mean the composition of f and g, where the output of g is used as the input of f.

This notation is sometimes used:
$(f \circ g) \equiv f(g(x)$

 

[HallsofIvy]

The notation fg normally means the product of f and g, not their composition.

(fg)(x) $\equiv$ f(x) * g(x)

When someone writes f(g(x)), they mean the composition of f and g, where the output of g is used as the input of f.

This notation is sometimes used:
$(f \circ g) \equiv f(g(x)$

Just to be nitpicky that should be either $(f\circ g)(x)\equiv f(g(x))$ or $(f\circ g)= f(g)$.

 

[adjacent]

The notation fg normally means the product of f and g, not their composition.

(fg)(x) $\equiv$ f(x) * g(x)

When someone writes f(g(x)), they mean the composition of f and g, where the output of g is used as the input of f.

This notation is sometimes used:
$(f \circ g) \equiv f(g(x)$

But I usually assume that $fg(x)$ is not the product but I put the $g(x)$ in $f$.
For example,to make sense,
$f(x)=x+1$
$g(x)=x+2$
Find $fg(x)$
What I do is
Just put g(x) in the function f.that is, (g(x))+1 or (x+2)+1
This is where my doubt persist.

 

[CompuChip]

I'm not sure fg(x) is standard notation, maybe it's best to avoid it and either write $f(g(x)) = (f \circ g)(x)$ or $f(x)g(x)$, depending on what you mean. If your teacher uses the notation fg(x), you should ask them to define it and not assume that the same definition is used in another course.

 

[adjacent]

I'm not sure fg(x) is standard notation, maybe it's best to avoid it and either write $f(g(x)) = (f \circ g)(x)$ or $f(x)g(x)$, depending on what you mean. If your teacher uses the notation fg(x), you should ask them to define it and not assume that the same definition is used in another course.

I will ask them

 

[Mark44]

Just to be nitpicky that should be either $(f\circ g)(x)\equiv f(g(x))$ or $(f\circ g)= f(g)$.

Yes, you're right. That's what I meant, but was a bit sloppy.

 

[adjacent]

I read from a book about algebra today
"Teach it yourself"
It says fg(x) is same as f(g(x)).It is a mistake to think that fg is multiplication.
Why is this different?

 

[Mark44]

Can you provide the name of the author and possibly a link to the book?

If this book says that fg(x) means f(g(x)), then what notation does the book use for the product of f and g, evaluated at x?

Every book I've ever seen uses f(g(x)) or $(f \circ g)(x)$.

 

[Tobias Funke]

Maybe it was an "advanced algebra" book and f and g were permutations of some set. That's the only time I've seen fg for a composition, but in that context it seems like very common notation (I don't think I've seen an algebra book that doesn't use the notation, now that I think about it).

 

[DrewD]

Maybe it was an "advanced algebra" book and f and g were permutations of some set. That's the only time I've seen fg for a composition, but in that context it seems like very common notation (I don't think I've seen an algebra book that doesn't use the notation, now that I think about it).

Agreed. The text we used first defined the notation as such and made a comment that this notation is common in algebra, but far from universal.

Edit: To the OP, this notation is used in situations (such as groups of functions) where there will be no confusion between multiplication and composition. If there will be no confusion, why use the extra notation?

 

[Mark44]

I might be wrong, but the context given in the OP makes me think this was not an advanced algebra problem.

 

[adjacent]

http://www.teachyourself.co.uk/ .There are no link to the book directly.The author is
P.Abott and Huge Neill.
The book says:

Its a common mistake to think that fg means multiply the rules for f and g together you should think of fg as being 'f of g' or f[g(x)]-So fg means use g rule first and then f rule.

They says to think fg as f[g(x)] and its a mistake to think fg as multiply rules os fg.What's going on?

This is just an elementary algebra book

 

[DrewD]

I'm assuming that adjacent's post was removed due to a link? It sounds like the book is being silly. It really depends on the context. For example
$(fg)'=f'g+g'f$
This is multiplication.

Let $f$ and $g$ be linear functions. Under the operation of composition, they form a group. Therefore, if
$fg=h$
then $h$ is a linear function.
This is composition.

There is nothing "going on", it is just a different use of the same notation. The same thing happens with $\times$ which is used for normal scalar multiplication with young kids and is the cross product with vectors (there are probably other uses too). Is this instance, it seams strange that the authors would choose this notation (I took a quick look on Amazon at the two books that it could be by P. Abbott and Hugh Neill) since it is not common in my experience in elementary algebra or calculus.

 

[Mark44]

I'm assuming that adjacent's post was removed due to a link?

adjacent removed his own post, for some reason. Since it is germane to the discussion, I have undeleted it.

 

[adjacent]

adjacent removed his own post, for some reason. Since it is germane to the discussion, I have undeleted it.

I did not delete my post.What happened?

 

[Mark44]

I did not delete my post.What happened?

Your post had been deleted, and there was a note that you had edited your post. I assumed that this meant you had deleted your post. If you didn't delete it, do you remember what you did to it?