Examples of using Inverse function in English and their translations into Thai
{-}
-
Colloquial
-
Ecclesiastic
-
Ecclesiastic
-
Computer
And this is the inverse function.
For the inverse function, 0 gets mapped to 4.
Because this is the only possible inverse function.
Only one inverse function which is true.
That's right. You need to check if it's an inverse function.
Or the inverse function is mapping us from 4 to 0.
So let's apply our f inverse function to this.
The inverse function, if you take f inverse of 4, f inverse of 4 is equal to 0.
And so we now have our inverse function as a function of x.
That if f is invertible, it only has one unique inverse function.
What does the inverse function look like, as a function of x?
We use the definition of invertibility that there exists this inverse function right there.
We tried before to have maybe two inverse functions, but we saw they have to be the same thing.
And that unique solution, if you really care about it, is going to be the inverse function applied to y.
Now, just out of interest, let's graph the inverse function and see how it might relate to this one right over here.
So if it's not unique, let's say that there's two functions that satisfy our two constraints that can act as inverse functions of f.
Such that this inverse function, the composition of the inverse with the function, is equal to the identity function. .
So given that f is invertible, we know that there is this f inverse function, and I can apply that f inverse function.
So since we only have one inverse function and it applies to anything in this big upper-case set y, we know we have a solution.
And the inverse and the function in the composition of the function, with the inverse function, should be the identity on y.
The definition of this inverse function is that when you take the composition with f, you're going to end up with the identity function. .
Solve for x in terms of y, and that's essentially your inverse function as a function of y, but then you can rename it as a function of x.
In the first inverse function video, I talked about how a function and their inverse-- they are the reflection over the line y equals x.
And because it's only one inverse function, and functions only map to one value in this case, then we know this is a unique solution.
So, if I take the inverse function on both sides of this equation, where some element over here in y, and I'm taking the inverse function to get to some element in x, what's this going to be equal to?
Self-preservation instincts intended for the inverse function, at the moment do not work or appear conditionally, for example, only at the verbal level, and at the behavioral one are absent.
So this is the inverse function right here, and we have written it as a function of y, but we can just rename the y as x so it's a function of x.
So if I apply the f inverse function to both sides of the equation, this right here's an element in y, and this is the same element in y.
And then we essentially apply the inverse function to both sides of this equation and say, look you give me any y, any lower-case cursive y in this set y, and I will find you a unique x.
Or if we want to write it in terms, as an inverse function of y, we could say-- so we could say that f inverse of y is equal to this, or f inverse of y is equal to the negative square root of y plus 2 plus 1, for y is greater than or equal to negative 2.