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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.
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FranIt 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)
