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What else can I help you with?
In the function G Fx G depends on F and F depends on x?
true
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 are the compsition of function?
A composition function, regarding two functions, is when you apply the first function on the second function on an argument. Bear in mind that a single, unaltered function is when you apply said function to an argument; a composition function simply applies the result of an application as an argument to another function. For example, if one function is defined as f(x) = x + 4 and another is defined as g(x) = 2x, the composition of the two (where f is applied to g) is f(g(x)) = 2x + 4. Note that composition is not commutative; that is, f(g(x)) is not necessarily equivalent to g(f(x)), unless if the functions are either the same or inverses of each other, in which case the result will be the argument; f(f-1(x)) = f-1(f(x)) = x.
What is the Derivative chain rule of (4-x)^3?
The chain rule states that the derivative of f(g(x)) is f'(g(x))⋅g'(x). In other words, it helps us differentiate *composite functions*. For example, sin(x²) is a composite function because it can be constructed as f(g(x)) for f(x)=sin(x) and g(x)=x².
Determine the inverse g(x) of the function f(x) = (1+(4/x)), stating its domain and range. Verify that f(g(x)) = g(f(x))=x and that g′(f(x)) = (1/(f′(x))?
Let f(x) = y y = 1 + (4/x) Now replace y with x and x with y and find equation for y x = 1 + (4/y) (x-1) = (4/y) y = 4/(x-1) This g(x), the inverse of f(x) g(x)= 4/(x-1) The domain will be all real numbers except when (x-1)=0 or x=1 So Domain = (-∞,1),(1,+∞) And Range = (-∞,0),(0,+∞) f(g(x)) = f(4/(x-1)) = 1 + 4/(4/(x-1)) = 1+(x-1) = x g(f(x)) = g(1+(4/x)) = 4/((1+(4/x))-1) = 4/(4/x) = x So we get f(g(x)) = g(f(x)) Notice the error in copying the next part of your question It should be g'(f(x)) = 1/(f'(g(x))) g'(f(x)) = d/dx (g(f(x))) = d/dx (x) = 1 f'(g(x)) = d/dx (f(g(x))) = d/dx (x) = 1 1/[f'(g(x))] = 1/1 = 1 g'(f(x)) = 1/f'(g(x)) ( Notice the error in copying your question)
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 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.
How can you tell if a equation is inverse?
Graph that equation. If the graph pass the horizontal line test, it is an inverse equation (because the graph of an inverse function is just a symmetry graph with respect to the line y= x of a graph of a one-to-one function). If it is given f(x) and g(x) as the inverse of f(x), check if g(f(x)) = x and f(g(x)) = x. If you show that g(f(x)) = x and f(g(x)) = x, then g(x) is the inverse of f(x).
