MHB What Does Function Composition Mean in Mathematics?

[tmt1]

Hello,

I have been asked to to find the functions

$$f \omicron g$$

and

$$f \omicron f$$

and so on where f(x) and g(x) are both functions.

What does this mean and where can I find resources to study it (youtube videos etc.). I can't google because I don't know the proper terminology.

Thanks.

Tim

 

[I like Serena]

Hello,

I have been asked to to find the functions

$$f \omicron g$$

and

$$f \omicron f$$

and so on where f(x) and g(x) are both functions.

What does this mean and where can I find resources to study it (youtube videos etc.). I can't google because I don't know the proper terminology.

Thanks.

Tim

Hi tmt!

It's the function composition operator.

$(f\circ g)(x)$ is defined as $f(g(x))$.
See the wiki page I referred to for examples.

 

[Opalg]

I have been asked to to find the functions

$$f \omicron g$$

and

$$f \omicron f$$

and so on where f(x) and g(x) are both functions.

What does this mean and where can I find resources to study it (youtube videos etc.).

The composition symbol $\circ$ is used to denote a "function of a function". You can find a good simple introduction to it here.