Your friend used some simple functions and found that (f⁰g)(x)=(g⁰f)(x) , and concluded that function composition is commutative. Give an example to show that your friend is mistaken.

Respuesta :

The composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.

What is meant by function composition?

In mathematics, function composition is an operation in which two functions, f and g, generate a new function, h, in such a way that h(x) = g(f(x)). This means that function g is being applied to the function x. So, in essence, a function is applied to the output of another function.

Define fog, the composition of f and g, as (fog)(x) = f(g(x)) for functions f and g. g should be applied to x. If fog(x) = x and gof (x) = x for all x values in the domain of f and g, then they are inverse functions.

In math, the domain (the x-values) of one function becomes the range (the y-value answers) of the next function. Composition notation is as follows: (f o g)(x) = f(g(x)) and exists read “f composed with g of x” or “f of g of x”.

To learn more about function composition refer to:

https://brainly.com/question/20759060

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