0
What else can I help you with?
What is composite function in calculus?
composite of a function is fog(x)=f(g(x))
If F(x) x plus 2 and G(y) what is the domain of G(F(x))?
It is necessary to know the domain of x and also what the function G(y) is before it is possible to answer the question.
How do you get a function of a function?
A function is a mapping from one set of numbers (domain) to another (range). The mapping need not be linear: it can be any mathematical function. That is, for every number in the domain the function provides a rule which allows you to calculate another number.If, then, you devise another function which is a mapping from the range of the first function to some other set, you have a function of a function.For example, suppose the first function, f, is "add 1" and the second function, g, is "square the number."Then the functiong of f = g[f(x)] = g[x+1] = [x+1]2 = x2 + 2x + 1however, note thatf of g = f[g(x)] = f[x2] = x2 + 1This illustrates that f of g is not the same as g of f.
Why can't the range of a function ever be equal to zero?
It most certainly can. In fact it can be quite a useful function. If you want to suppress one function, f(x), over part of its domain you could define another function, g(x) that is equal to zero over that part of the domain and then study the function: h(x) = f(x)*g(x) where both are defined = f(x) otherwise. You may want to do this if f(x) is ill-behaved over a part of its domain.
How can we use composite functions to check whether two different functions are inverses?
To determine if two functions ( f(x) ) and ( g(x) ) are inverses of each other, we can use composite functions. Specifically, we evaluate ( f(g(x)) ) and ( g(f(x)) ). If both compositions yield the identity function, meaning ( f(g(x)) = x ) and ( g(f(x)) = x ) for all ( x ) in their respective domains, then ( f ) and ( g ) are indeed inverses of each other.
What is composite function in calculus?
composite of a function is fog(x)=f(g(x))
What is the domain of the composite function GFX equals 2-x?
Given the function g(f(x)) = 2-x, you can find the domain as you would with any other function (i.e. it doesn't matter if it's composite). The output, however, has to be a real number. With this function, the domain is all real numbers. If you graph it, you see that the function is defined across the entire graph, wherever you choose to plot it.
What is f(g(x))?
Provided that the range of g(x) is the domain of f(x) then it is the composite function, called f of g of x.Note that f(g(x) ) is not the same as g(f(x).For example, if f(x) = x + 2 and g(x( = 3*x for real x, thenf(g(x)) = f(3*x) = 3*x + 2while g(f(x)) = g(x + 2) = 3*(x + 2) = 3*x + 6
If F(x) x plus 2 and G(y) what is the domain of G(F(x))?
It is necessary to know the domain of x and also what the function G(y) is before it is possible to answer the question.
Explain what a composite function is in terms of input and output?
A composite function is created when the output of one function becomes the input for another function. For two functions ( f ) and ( g ), the composite function ( (f \circ g)(x) ) means you first apply ( g ) to the input ( x ), and then take the output of ( g ) and apply ( f ) to it. In essence, you are chaining the functions together, transforming the initial input through both functions in sequence. The result is a new function that encapsulates the process of both transformations.
Is x the numbers that are domains of both f and g in the function fgx?
No. The set of x-values are the domain for only g. This will result in a set of images, which will be g(x). This set of g(x) values are the domain of f.
How do you get a function of a function?
A function is a mapping from one set of numbers (domain) to another (range). The mapping need not be linear: it can be any mathematical function. That is, for every number in the domain the function provides a rule which allows you to calculate another number.If, then, you devise another function which is a mapping from the range of the first function to some other set, you have a function of a function.For example, suppose the first function, f, is "add 1" and the second function, g, is "square the number."Then the functiong of f = g[f(x)] = g[x+1] = [x+1]2 = x2 + 2x + 1however, note thatf of g = f[g(x)] = f[x2] = x2 + 1This illustrates that f of g is not the same as g of f.
What is meant by f of g of x Specifically address the domain and range?
You would have been given a function for f(x) and another function for g(x). When you want to find f(g(x)), you put the function for g(x) wherever x occurs in f(x). Example: f(x)=3x+2 g(x)=x^2 f(g(x))=3(x^2)+2 I'm not sure what you mean by address domain and range. They depend on what functions you're given.
2.If fx 12x and gx 3 x find and simplify the defining equation of the composition function f circle g.?
The composite function f of g is also expressed as f(g(x)). In this case, it would be 12(3x), or 36x.
Why can't the range of a function ever be equal to zero?
It most certainly can. In fact it can be quite a useful function. If you want to suppress one function, f(x), over part of its domain you could define another function, g(x) that is equal to zero over that part of the domain and then study the function: h(x) = f(x)*g(x) where both are defined = f(x) otherwise. You may want to do this if f(x) is ill-behaved over a part of its domain.
What is the domain of the function G of F of x when F of x equals 8 minus x G of y equals square root of y G of F of x equals square root of 8 minus x?
x
How do you start composing a mathematical function?
To start composing a mathematical function, first identify the two functions you wish to combine, typically denoted as ( f(x) ) and ( g(x) ). The composition of these functions is expressed as ( (f \circ g)(x) = f(g(x)) ), meaning you apply the function ( g ) to ( x ) first, and then apply the function ( f ) to the result of ( g(x) ). Ensure that the output of the inner function ( g(x) ) is within the domain of the outer function ( f ). Finally, simplify the resulting expression if possible.
