## Quick Reference

**relative product**) A method of combining functions in a serial manner. The composition of two functions *f* : *X* → *Y* and *g* : *Y* → *Z* is the function *h* : *X* → *Z* with the property that *h*(*x*) = *g*(*f*(*x*) This is usually written as *g* ° *f*. The process of performing composition is an operation between functions of suitable kinds. It is associative, and identity functions fulfill the role of units.

*f* : *X* → *Y* and *g* : *Y* → *Z*

*h* : *X* → *Z*

*h*(*x*) = *g*(*f*(*x*)

If *R* denotes the set of real numbers and *f* : *R*→*R*, *f*(*x*) = sin(*x*) *g* : *R*→*R*, *g*(*x*) = *x*^{2} + 3 then *f*° *g* is the function *h*: *h* : *R*→*R*, *h*(*x*) = sin(*x*^{2} + 3)

*f* : *R*→*R*, *f*(*x*) = sin(*x*)

*g* : *R*→*R*, *g*(*x*) = *x*^{2} + 3

*h* : *R*→*R*, *h*(*x*) = sin(*x*^{2} + 3)

The idea of composition of functions can be extended to functions of several variables.

*n* into parts *a*_{1}, *a*_{2},… *a*_{k} in which the ordering is significant and in which*n* = *a*_{1} + *a*_{2} + … + *a** _{k}*where each

*a*

*is a positive integer. It is thus similar to a partition (see covering) but in a partition the ordering is not significant. In general the number of compositions of*

_{i}*n*is 2

*.*

^{n−1}*n* = *a*_{1} + *a*_{2} + … + *a*_{k}

**From:**
composition
in
A Dictionary of Computing »

*Subjects:*
Computing.