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ZeroPivot
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can a function that's not inversable be inversible in certain interwalls. is it ok to say its inversable in this specific intervall or can't the function ever be called inversible?
HallsofIvy said:Yes, but technically, it wouldn't be the same function.
For example, [itex]f(x)= x^2[/itex]is not "invertible" because it is neither "one to one" nor "onto". However, if we restrict the domain to the "non-negative real numbers" then its inverse is [itex]\sqrt{x}[/itex]. If we restrict the domain to the "non-positive real numbers" then its inverse is [itex]-\sqrt{x}[/itex].
However, the domain of a function is as much a part of its definition as the "formula". That is, "[itex]f(x)= x^2[/itex], for x any real number", "[itex]g(x)=x^2[/itex], for x any non-negative real number", and [itex]h(x)= x^2[/itex], for x any non-negative real number" are three different functions. The first does not have an inverse, the last two do.
"Inversible" is not a word - the one you want is invertible.ZeroPivot said:can i say function y=x^2 is inversible for x E [0 ,4] ?
Mark44 said:"Inversible" is not a word - the one you want is invertible.
An inverse function is a mathematical operation that undoes another function. It is essentially the "reverse" of a function and is denoted by f^-1(x).
A function must be one-to-one (injective) in order to have an inverse. This means that each input corresponds to a unique output and no two inputs have the same output.
The notation for an inverse function is f^-1(x), with the "^-1" indicating that it is the inverse of the original function f(x).
No, not all functions have an inverse. Only one-to-one functions have inverses.
To find the inverse of a function, switch the x and y variables and solve for y. The resulting equation will be the inverse function, f^-1(x).