Composition of function

Composition of Functions

Two functions f:ABf:A→B and g:BCg:B→C can be composed to give a composition gofgof. This is a function from A to C defined by (gof)(x)=g(f(x))(gof)(x)=g(f(x))

Example

Let f(x)=x+2f(x)=x+2 and g(x)=2x+1g(x)=2x+1, find (fog)(x)(fog)(x) and (gof)(x)(gof)(x).

Solution

(fog)(x)=f(g(x))=f(2x+1)=2x+1+2=2x+3(fog)(x)=f(g(x))=f(2x+1)=2x+1+2=2x+3

(gof)(x)=g(f(x))=g(x+2)=2(x+2)+1=2x+5(gof)(x)=g(f(x))=g(x+2)=2(x+2)+1=2x+5

Hence, (fog)(x)(gof)(x)(fog)(x)≠(gof)(x)

Some Facts about Composition

  • If f and g are one-to-one then the function (gof)(gof) is also one-to-one.
  • If f and g are onto then the function (gof)(gof) is also onto.
  • Composition always holds associative property but does not hold commutative property.

Author: Deepak Chahar

Leave a Reply

Your email address will not be published. Required fields are marked *