What is function composition?

2 Answers
Sep 26, 2015

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

Example:

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

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

If we substitute:

#-x+5=t => x=5-t#

#fdiamondg=f(t)=2(5-t)+3=10-2t+3=13-2t#
#fdiamondg=13-2x#

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

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

#2x-3=t => x=(t+3)/2#

#gdiamondf=g(t)=-((t+3)/2)+5=-t/2+7/2#

#gdiamondf=-x/2+7/2#

Refer to explanation

Explanation:

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