0
Y = 1/X2
==============Can it pass the line test?
* * * * *
That is not the inverse, but the reciprocal. Not the same thing!
The inverse is y = sqrt(x). Onless the range is resticted, the mapping is one-to-many and so not a function.
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∙ 11y ago
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Does every function have an inverse that is a function?
No. A simple example of this is y = x2; the inverse is x = y2, which is not a function.
What is the inverse of y x2?
Y = X2 Inverse. Y = 1/X2 ======
Is the inverse of the function y equals x2 still a function?
No. If you invert that function, it will produce an equation that gives you two return values for one input value. This does not meet the definition of a function.
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 kind of symmetry indicates that a function will not have an inverse?
If a function is even ie if f(-x) = f(x). Such a function would be symmetric about the y-axis. So f(x) is a many-to-one function. The inverse mapping then is one-to-many which is not a function. In fact, the function need not be symmetric about the y-axis. Symmetry about x=k (for any constant k) would also do. Also, leaving aside the question of symmetry, the existence of an inverse depends on the domain over which the original function is defined. Thus, y = f(x) = x2 does not have an inverse if f is defined from the real numbers (R) to R. But if it is defined from (and to) the non-negative Reals there is an inverse - the square-root function.
Does every function have an inverse that is a function?
No. A simple example of this is y = x2; the inverse is x = y2, which is not a function.
What is the inverse of y x2?
Y = X2 Inverse. Y = 1/X2 ======
Is the inverse of the function y equals x2 still a function?
No. If you invert that function, it will produce an equation that gives you two return values for one input value. This does not meet the definition of a function.
Which functions do not have an inverse?
y = x2 where the domain is the set of real numbers does not have an inverse, because the square root function is a one-two-two mapping (except at 0). Any polynomial with more than one root, over the reals, has no inverse. y = 1/x has no inverse across 0. But it is possible to define the domain so that each of these functions has an inverse. For example y = x2 where x is non-negative has the square root function as its inverse.
Is the inverse of a linear function not a function?
The inverse of a linear function is always a linear function. There are a few ways to approach this.To think about it, you can imagine flipping the x and y axes. Essentially this equates to turning the graph of the linear function on its side to reveal the new inverse function which is still a straight line.More rigorously, the linear function y = ax + b has the inverse equation x = (1/a)y - (b/a). This is a linear function in y.
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
Which function is the inverse function of y 5x - 4?
1
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()
How do you illustrate an inverse function?
Given a function, one can "switch" the variables x and y and then solve for y afterwards to determine the inverse function.
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.
What kind of symmetry indicates that a function will not have an inverse?
If a function is even ie if f(-x) = f(x). Such a function would be symmetric about the y-axis. So f(x) is a many-to-one function. The inverse mapping then is one-to-many which is not a function. In fact, the function need not be symmetric about the y-axis. Symmetry about x=k (for any constant k) would also do. Also, leaving aside the question of symmetry, the existence of an inverse depends on the domain over which the original function is defined. Thus, y = f(x) = x2 does not have an inverse if f is defined from the real numbers (R) to R. But if it is defined from (and to) the non-negative Reals there is an inverse - the square-root function.
What is the difference between a reciprocal function and an inverse function?
A reciprocal function will flip the original function (reciprocal of 3/5 is 5/3). An inverse function will change the x's and y's of the original function (the inverse of x<4,y>8 is y<4, x>8). Whenever a function is reflected over the line y=x, the result is the inverse of that function. The y=x line starts at the origin (0,0) and has a positive slope of one. All an inverse does is flip the domain and range.
