help mathfags!

>>347858

Make the inverse of G(x), you do that by stting the g(x), which for an x is the function's result- in other words its y, as y and form the resulting equation y=5/ 2x+8 so that x is alone on one side, the other side then is your inverted function- for which you can then swap x and y around again so you put in an x again, not an y (doesn't formally change anything, just pure variable renaming) .

AoB = A(B(x)), with a given value x put it first in B, then use this result as input for A.
In this case there no specific value, so put in the whole inverted G as x into H and simplify.

>>347886
Why write "hog" when "h(g(x))" is just as concise?

File: __madotsuki_yume_nikki__sample-451dd3bfc7418cf2483dafce1249664f.jpg (78KB, 850x850px) Image search: [Google]

78KB, 850x850px

thx m8s i now understand <3

>>347887

It's not an "o", the letter, but a special mathematical symbol, a small circle, like the degree symbol ° but centered.
As to why it exists in the first place... in maths you like abbreviating, especially when chaining multiple functions by using it you save brackets and it look more tidy,
(G o H o I)(x), then even written simply as G o H o I, looks better than (G(H(I(x))). Easier to read too.

>>347894
It's also because composition is an operator just like + or *, and ∘ is better for writing properties like f∘(g∘h)=(f∘g)∘h just like you would write x+(y+z)=(x+y)+z

>>347939
>>347894
To me, f(g(h(x))) looks normal and easily-understood, and fogoh(x) is the one that looks weird.

I think the thing I'm finding weird about it is that using an infix operator implies commutativity (which is why the division operator is only used before PEMDAS is taught, I think), and that every other infix operator in use will accept numbers, whereas the LHS of the circle doesn't because "5" is not a function: f(x)=5x is a function, and it's just coincidence that f(x) and 5(x) are written the same, 5(x) being shorthand for 5*(x).

But in any case mathematics isn't going to change just because I don't like it, so thank you for explaining it to me.

>>347963
>To me, f(g(h(x))) looks normal and easily-understood, and fogoh(x) is the one that looks weird.
It may look weird when you use it in an expression, but as I said, it makes more sense if you're expressing properties of the composition of functions itself, especially in the context of algebraic structures

>I think the thing I'm finding weird about it is that using an infix operator implies commutativity
Subtractions in general and matrix multiplications are not commutative

>and that every other infix operator in use will accept numbers
The cross product operator accepts vectors, the various logical operators accept truth values, set operators accepts sets, etc.