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If f(x) is a function, the inverse may, or may not, be a function. In math, quite often it is possible, and sensible, to restrict the original function to a certain range of numbers, within which the inverse is well-defined.The function f(x) has an inverse (within a certain range) if it is strictly monotonous within that range.
It will be only if f(x) is a bijection - that is, one-to-one and onto. You may be able to make f(x) a bijection by altering its domain. For example, f(x) = sin(x), where x is measured in degrees, is a function defined for all real x. The inverse mapping is g(x) = arcsin(x) or sin-1(x). Then g(x) is not a function because g(0.5) = 30 degrees or 150 deg or (30+k*360) deg or (150+k*360) deg where k is any integer. That is, g(0.5) has infinitely many values and so cannot be a function. However, if the domain of f(x) is restricted to -90 to 90 degrees, then g(x) is a function.
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What is the inverse of the function f(x) 4x 8?
The inverse for f(x) = 4x + 8 isg(x) = x/4 - 2
What is the inverse of an even function?
An even function cannot have an inverse.If f(x) = y, then if f is an even function, f(-x) = y.Then, if g were the inverse function of f, g(y) would be x as well as -x.But a one-to-many relationship is not a function.
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).
What function is the inverse of a quadratic function?
If the quadratic function is f(x) = ax^2 + bx + c then its inverse isf'(x) = [-b + +/- sqrt{b^2 - 4*(c - x)}]/(2a)
If 2 1 is an ordered pair of the function F x what must be an ordered pair of the inverse of F x?
(1,2)
What is an inverse function?
A function that, given X, will produce Y has an inverse function that will take Y and produce X. More formally:If f(x)=y, then f-1(y)=xWhere f-1() denotes the inverse function of f()
If the function g is the inverse of the function f, then f(g(x))=?
= x
What is the inverse of the function f(x) 4x?
if f(x) = 4x, then the inverse function g(x) = x/4
What is inverse of a function?
Simply stated, the inverse of a function is a function where the variables are reversed. If you have a function f(x) = y, the inverse is denoted as f-1(y) = x. Examples: y=x+3 Inverse is x=y+3, or y=x-3 y=2x+5 Inverse is x=2y+5, or y=(x-5)/2
What is the inverse of the function f(x) 2 - x?
The inverse for f(x) = 4x + 8 isg(x) = x/4 - 2
What is an inverse relation and how do you find an inverse relation given a function?
Given a function that is one-to-one and onto (a bijection), an inverse relationship is a function that reverses the action of the first function.A simple example to illustrate:if f(x) = x + 2, then g(x) = x - 2 is its inverse. fg(x) = x = gf(x).To find an inverse relationship of a function f(x)write y = f(x) as a function of xswap x and ymake the [new] y the subject of the formulathat is the inverse function.Going back to f(x) = x + 2write y = x + 2swap: x = y + 2make y the subject of the above equation: y = x - 2and so f'(x) is x - 2 where f'(x) represent the inverse of f(x).
What is the inverse of the function f(x) 4x 8?
The inverse for f(x) = 4x + 8 isg(x) = x/4 - 2
What is the inverse of an even function?
An even function cannot have an inverse.If f(x) = y, then if f is an even function, f(-x) = y.Then, if g were the inverse function of f, g(y) would be x as well as -x.But a one-to-many relationship is not a function.
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).
What are the inverses of hyperbolic functions?
If f(x)=y, then the inverse function solves for y when x=f(y). You may have to restrict the domain for the inverse function to be a function. Use this concept when finding the inverse of hyperbolic functions.
Function and inverse of function graph is the same?
In general the function and it inverse are not the same and do not have the same graph. If we look at a special function f(x)=x, it is equal to its inverse and the graph is the same. Think of the inverse of a function as changing all the x's to y's and vice versa. Well, in the function f(x)=x, all the x's are already y's and vice versa so it is its own invese.
What is the inverse of the function f of x equals x to the power of one over x?
The inverse is not a function because it fails the vertical line test.
