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Answer these questions:
Describe the relationship of input and output values for a composite functions.
Is the inverse of a function always a function? Explain.

Respuesta :

Edufirst
1) Describe the relationship of input and outpunt values for a composite functions.

The composition of the functions f(x) and g(x) is defined as:

(f ° g) (x) = f [g(x) ].

That means that the output of the function g(x) is the input of the function f(x).

2) Is the inverse of a function always a function?

No, the inverse of a function is not always a function.

Remember that a function cannot have two different outputs for one or more input.

The reason is that if the original function has two or more inputs that result in a same output, when you inverse the original function, the outputs of the original are the inputs of the inverse function and the inputs of the original are the outputs of the inverse. That implies that the inverse function would have some inputs related with more than one output, which is the negation of a function.


aksnkj

The output of f(x) is the input of the gof(x) function (composite function). And inverse of a function is not always a function.

Composite function is a combination of two or more functions.

Let f(x) be a function and g(x) be another function. So, fog(x) or gof(x) will be the composite functions.

The function gof(x) can be written as,

[tex]gof(x)=g(f(x))[/tex]

Here, the output of f(x) is the input of the gof(x) function.

Function is a type of relation in which one element of domain is related to only one element of range or it has a unique image.

Now, not every inverse of a function is a function. This is because in a function, multiple elements of domain can be attached to one element in the range. While taking the inverse, domain will become range. So, one element of the domain of inverse will have multiple images. Thus, inverse is not compulsorily a function.

Therefore,  the output of f(x) is the input of the gof(x) function (composite function). And inverse of a function is not always a function.

For more details, refer to the link:

https://brainly.com/question/10300045

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