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If there are two functions: f(x) and g(x), and the 2nd domain is within the range of the 1st, it can be defined as a new function that associates each element of the domain of f(x) with the value of g[f(x)].

(g o f) (x) = g [f(x)] = g (2x) = 3 (2x) +1 = 6x + 1

(g o f) (1) = 6 · 1 + 1 = 7

## Domain

D(g o f) = {x Df / f(x) Dg}

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4.9 (23 reviews)
Shane
£25
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1st lesson free!
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Jamie
£25
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1st lesson free!
5 (17 reviews)
Matthew
£30
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1st lesson free!
4.9 (12 reviews)
Petar
£40
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1st lesson free!
5 (14 reviews)
Harinder
£15
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1st lesson free!
4.9 (17 reviews)
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## Properties

Associative:

f o (g o h) = (f o g) o h

Not commutative.

f o g ≠ g o f

The identity element is the identity function, i(x) = x.

f o i = i o f = f

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