Question

what is composition of function?
I forget all about it

Answer 1

a composition is when you use one thing to compose (build, create, construct) another thing

Answer 2

if youve ever built a model car; the instructions are a composition of functions; each new step is dependant upon the one before it

Answer 3

Suppose you have two functions, f(x) and g(x), then you can do the composite function,
\[(f\circ g)(x)=f(g(x))\]
Let's try an example. If f(x)=2x+3, and g(x)=x^2+1, then,
\[(f\circ g)(x)=f(g(x))=2g(x)+1=2(x^2+1)+3=2x^2+5\]
This is the composition of f(x) with g(x).

Answer 4

ok thank you so much

Answer 5

You should be carefull with the function domains, because in the case I proposed the image space of g(x) must be in the domain space of f(x).

Answer 6

You're welcome.

Answer 7

but we can say that domain is that which doesnt disturb our function
actually I didn't understand domain

Answer 8

The domain of a function is the collection of points where you can calculate your function. For example,
\[y=2x+3\]
It can be calculated for every real x, so its domair is all reals.
But suppose you have the following function,
\[y=\frac{2}{x+3}\]You know that we cannot divide by zero, so the domain of this function is all reals except x=-3, because in x=-3, we have 2/0 and this value doesn't exist.

Answer 9

so how can write its domain

Answer 10

You can write the domain of a specific function if you know its expression. For example,
\[y=x+3\Rightarrow D=\mathbb{R}\]
or equivalently,
\[ D=\{\mathbb{x:x\in R}\}\]For the second case, I wrote before,
\[D=\{x: x \in \mathbb{R} \wedge x\neq-3\}\]

Answer 11

thank you

Answer 12

I am conguse in composition of function
lemme show you a example
tell me is it a composition of function f(x)=x2+1
g=x,h=x2+1
g(h(x))=x2+1
what is this
is this a composition of fuction?