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In the function g(f(x)) depends on gand g depends on x?

Function "f" depends on "x", and function "g" depends on function "f".


In the function G F x G depends on F and F depends on x?

true


In the function G Fx G depends on F and F depends on x?

true


In the function G(F(x)) F depends on G and G depends on x?

In the function G(F(x)), F is a function that relies on G, creating a circular dependency where G's output influences F's behavior. Simultaneously, G itself is dependent on the input x, indicating that changes in x will affect G's output. This interdependence can lead to complex relationships and potentially recursive behavior, depending on how F and G are defined. Care must be taken to ensure that such dependencies do not lead to infinite loops or undefined outcomes.


If the function g is the inverse of the function f, then f(g(x))=?

= x


What notation represents a function as f x instead of y?

'Y' is a function 'f' of 'x': Y = f(x) . 'Z' is a function 'g' of 'y': Z = g [ f(x) ] .


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


What is the integral of the quantity of the derivative with respect to x of the function f times another function of x defined as g subtracted by g prime times f divided by f times g with respect to x?

∫ [f'(x)g(x) - g'(x)f(x)]/[f(x)g(x)] dx = ln(f(x)/g(x)) + C C is the constant of integration.


What is the inverse of the function f(x) 4x?

if f(x) = 4x, then the inverse function g(x) = x/4


What is the integral of the quantity of the derivative with respect to x of the function f times another function of x defined as g subtracted by g prime times f divided by g squared with respect to x?

∫ [f'(x)g(x) - g'(x)f(x)]/g(x)2 dx = f(x)/g(x) + C C is the constant of integration.


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.


What is the integral of the derivative with respect to x of a function of x multiplied by another function of x with respect to x?

∫ f'(x)g(x) dx = f(x)g(x) - ∫ f(x)g/(x) dx This is known as integration by parts.