Inverse mode

Reciprocal

So that's a special case of a square di, diagonal matrix.

You can get rid of that negative by just putting a 1 over this whole thing.

And I want to calculate its inverse.

And so, there's a couple of ways to think about it.

Any real number will work here.

Or let me just write it a little bit cleaner.

So a, another way to think about it is, you're going to take the reciprocal of this and raise it, and raise it to the positive exponent.

I'll leave this for you to think about.

Or we could say, the function f maps us from 5 to negative 1.

For example the number zero does not have an inverse, right?

Here we just use x, but they are identical functions.

You just do some algebra.

Remember, you see a negative exponent, that just means the reciprocal of the positive exponent.

Well it's x to the third over 3.

Because we've essentially just swapped the x and the y.

Let's try to figure out what the inverse of f is.

For the regular function, 4 gets mapped to 0.

Our function is mapping 0 to 4.

So, like we've said in the first video, in the introduction to inverses, we're trying to find a mapping.

Let's think about what functions really do, and then we'll think about the idea of an inverse of a function.

What you'll find is it's actually very easy to solve for this inverse of f, and I think once we solve for it, it'll make it clear what I'm talking about.

Count from 10 down to zero.

We can then get a row vector of means just by taking that previous product, the row vector of sums.

So remember, whenever you see that negative, what my brain always does is say, I need to take the reciprocal here.

So another way you could've thought about this, another way you could've thought about this is 5 8ths to the negative 2 power.

Or another way to write it is we could say that f inverse of y is equal to negative y plus 4.

So we can call this we could say that this is equal to

That's where we've defined our function.

All distances and all times scale linearly with Hubble's constant.

So let's solve for x.

It don't know, there something wacky about that that the inverse of the number is really just the decimals

So let's see, if we have the y intercept is 4, it's going to be the exact same thing.

We're changing the division operation to a multiplication, and we're taking the reciprocal of the 7 4.

Or is there some other function?

We want to go through the elements in the original list in reverse order.

This is a function that is easy to compute in one direction, yet difficult to reverse, unless you have special information called the trap door.

Just like that.

Can you count backwards from 10? Who is the President of the United States?

I'll do direct variations on the left over here

And that will actually be really useful in the future when we talk about inverses and shifting functions.

Mutiny. Mutiny.

I'll do it in the same color this is equal to f inverse as a function of y.

They've constrained so that it's not a full U parabola.