What is function composition?

Question

What is function composition?

2 Answers

Impact of this question

12860 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-09-26T20:41:47

See the explanation.

Explanation:

Informal speaking: "it's a function of function".
When you use one function as a argument of the other function, we speak of the composition of functions.

$f (x) ⋄ g (x) = f (g (x))$ $f(x) diamond g(x) =f(g(x))$ where $⋄$ $diamond$ is composition sign.

Example:

Let $f (x) = 2 x - 3, g (x) = - x + 5$ $f(x)=2x-3, g(x)=-x+5$ . Then:

$f (g (x)) = f (- x + 5)$ $f(g(x))=f(-x+5)$

If we substitute:

$- x + 5 = t \Rightarrow x = 5 - t$ $-x+5=t => x=5-t$

$f ⋄ g = f (t) = 2 (5 - t) + 3 = 10 - 2 t + 3 = 13 - 2 t$ $fdiamondg=f(t)=2(5-t)+3=10-2t+3=13-2t$
$f ⋄ g = 13 - 2 x$ $fdiamondg=13-2x$

You can, however, find $g (f (x))$ $g(f(x))$

$g (f (x)) = g (2 x - 3)$ $g(f(x))=g(2x-3)$

$2 x - 3 = t \Rightarrow x = \frac{t + 3}{2}$ $2x-3=t => x=(t+3)/2$

$g ⋄ f = g (t) = - (\frac{t + 3}{2}) + 5 = - \frac{t}{2} + \frac{7}{2}$ $gdiamondf=g(t)=-((t+3)/2)+5=-t/2+7/2$

$g ⋄ f = - \frac{x}{2} + \frac{7}{2}$ $gdiamondf=-x/2+7/2$

Answer 2 · 2015-09-26T21:35:41

Refer to explanation

Explanation:

Combining two functions by substituting one function's formula in place of each $x$ $x$ in the other function's formula.
The composition of functions $f$ $f$ and $g$ $g$ is written $f o g$ $fog$ , and is read "f composed with g." The formula for $f o g$ $fog$ is written $(f o g) (x)$ $(fog)(x)$ .
The domain and range for the functions are $f : A \to B$ $f:A->B$ and $g : B \to C$ $g:B->C$

Science

Math

Humanities

... and beyond

What is function composition?

2 Answers

Explanation:

Explanation:

Related questions

Impact of this question