Rachit Kumar SaxenaManager-Editorial
What is Composition of Function?
The function composition is a function where two functions say that f and g generate a new function, say h, in such a way that h(x) = g(f(x)). This implies that the function g is extended to function x. So, essentially, a function is added to the output of a different function.
Symbol: It is often denoted as (goh)(x), where there is a small circle symbol. It cannot be substituted by a dot (.) since it would be the output of two functions, such as (g.f) (x).
Domain: f(g(x)) shall be interpreted as f of g of x. In the composition of (f o g) (x) the function domain f becomes g (x). The domain is set to all values that are used in the function.
Properties of the Composition of Functions
Associative Property: As for the associative properties of the function composition, if there are three functions f, g, and h, they are said to be associative if and only if;
Commutative Property: two functions f and g are said to be swapped with each other, if and only if;
g○f = f○g
A few more of the properties are:
- The one-to-one feature composition is still one-to-one.
- The two-on-function composition is still on
- The reciprocal of the composition of the two variables f and g is equivalent to the composition of the inverse of the two functions, such as (f○g)-1=(g-1○ f-1)
Composition of Function With Itself
It is necessary to compose a function on its own. Suppose f is a function, so the composition of the function f will be on its own.
(f○f)(x) = f(f(x))
Weightage of Composition Of Functions in Class 12
This concept is taught under the chapter Relations and Functions. You will learn about the different functions and their properties. The weightage of this topic is 8 marks in the final exam.
Illustrated Examples on Composition of Function
1. f(x) = 2x +1 and g(x) = -x^2, then find (g∘f)(x) for x = 2.
Solution:
Given,
f(x) = 2x+1
g(x) = -x^2
To find: g(f(x))
g(f(x)) = g(2x+1) = -(2x+1)^2
Now put x =2 to get;
g(f(2)) = -(2.2+1)^2
= -(4+1)^2
=-(5)^2
=-25
2. If f(x) = x – 3 and g(x) = 4x2 – 3x – 9, find(gof)(x)
Solution:
(g o f )(x) = g(f (x))
= 4(x — 3)2— 3(x — 3) — 9
=4(x2 — 6x +9)— 3(x — 3)— 9
= 4x2— 24x +36-3x +9-9
= 4x2— 27x +36
FAQs on Composition of Function
Q: How can you figure out the composition of a function?
(gf)(x) = g(f(x)), first add f(), then apply g ()
We will need to respect the domain of the first function.
Some functions may be decomposed into two (or more) simplified functions.
Q: Is the composition of an associative function?
Q: What are the features of the function composition?
Q: What is the composition of the function examples?
Q: How can you create a composite function?
News & Updates
Relations and Functions Exam
Student Forum
Popular Courses After 12th
Exams: BHU UET | KUK Entrance Exam | JMI Entrance Exam
Bachelor of Design in Animation (BDes)
Exams: UCEED | NIFT Entrance Exam | NID Entrance Exam
BA LLB (Bachelor of Arts + Bachelor of Laws)
Exams: CLAT | AILET | LSAT India
Bachelor of Journalism & Mass Communication (BJMC)
Exams: LUACMAT | SRMHCAT | GD Goenka Test