A composite function is formed when the output of the first function becomes the input of the second function.
Let f and g be functions and let x be the input of g. Then, g(x) is the output of function g.
g(x) is the input of function f and the output of function f is f(g(x))
f(g(x) is the composite function of f and g and it is defined as (f ∘ g)(x) = f(g(x))
We can also let x be the input of f. Then, f(x) is the output of function f.
f(x) is the input of function g and the output of function g is g(f(x))
g(f(x) is a composite function of g and f and it is defined as (g ∘ f)(x) = g(f(x))
Example
Let f(x) = x + 5 and let g(x) = x^{2}
Find g ∘ f and f ∘ gg(f(x)) = g(x + 5) = (x + 5)^{2}
= x^{2} + 5x + 5x + 25
= x^{2} + 10x + 25
f(g(x)) = f(x^{2}) = x^{2} + 5
Be careful ! g(f(x)) is not equal to f(g(x)) although it may in some cases.
Jan 18, 19 10:53 AM
This overtime calculator will help you figure out how much money earned for working overtime
New math lessons
Your email is safe with us. We will only use it to inform you about new math lessons.
Jan 18, 19 10:53 AM
This overtime calculator will help you figure out how much money earned for working overtime
Our Top Pages
Formula for percentage
Compatible numbers
Basic math test
Basic math formulas
Types of angles
Math problem solver
Algebra word problems
Surface area of a cube
Finding the average
Scale drawings
Everything you need to prepare for an important exam!
K-12 tests, GED math test, basic math tests, geometry tests, algebra tests.
Real Life Math Skills
Learn about investing money, budgeting your money, paying taxes, mortgage loans, and even the math involved in playing baseball.