You start with 3, 3 is being mapped by the function to 10.

When we're dealing with the standard function right there, if you input a 2, it gets mapped to a 2.

And then we take the derivative of the outside function or the derivative of the outside function with respect to the inner function.

So the derivative of x is just 1, times the second function, times e to the x, plus the first function, x, times the derivative of the second function.

So we're saying this function, when does this function equal 0?

So the function will say, you give me that, then I will map it to that member right there.

So first we'll do this inner function, this inner expression.

The composition of the inverse with the function has to become the identity matrix on x.

Then the composition of the function with the inverse has to be the identity function on Y.

That's all a function is.

That's what that function looks like.

And we know that we're dealing with, the function is concave upwards at this point.

So this is going to be equal to, this is the same thing as the composition of the identity function over x with g.

So this is equal to h composed with, or the composition of h with, the identity function over y with this right here.

HDR Layer from bracketing

That's what makes it a function.

It's going to give me an answer to what the function is.

So that's the function.

The function does not do this.

The function does not do that.

It's the exact same function.

The function is its own inverse.

So this is a valid function.

Let's go to this function.

The function will look something like this.

And it's being done by the function.

What does this function look like?

Now we have this function.

We just evaluated our function.

That's where we've defined our function.

And this is the inverse function.

So this does fit our kind of definition or our terminology for a function or a transformation as a mapping from one set to another.

If it's a continuous function, then the limit as z approaches 2 is going to be the function at 2.

Let's take the derivative of the inside.

So what's the derivative of the inside function?

They texted me back, It's called a syzygy.

What are the domain and range for that function?

If the function is continuous, we'd be done.

What is the derivative of this function?

And let s say the function looks something like

Say this was a function definition.

That's what the function f does.

They tell us this is our function definition.

So this function looks something like that.

I'm not drawing the actual function.