That's what the function f does.

Is f equal to the gradient of some function, capital F?

PROBLEM The function f(x) is graphed.

Let's say we have a function, f.

So given that f is invertible, we know that there is this f inverse function, and I can apply that f inverse function.

The function f(x) is defined as f(x) 49 (x 2).

We wrote before that f is a function.

If you imagine our box, the function f.

So you're an even function if and only if, f of f(x) is equal to f( x).

I'm just trying an arbitrary function f of x.

So f of x, that's just the function, right?

So this function right there is f of x.

So let's apply our f inverse function to this.

What is the outside function? f of y, x is equal to f of y.

Well, it tells us, that for any continuous function f,

And let's say I have some function f of x.

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So this vector right here, by our function, f, got mapped

So let's say that I have some function f of t.

Our function is f of x is equal to x squared.

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So let's say I had the function f of x. f of x is equal to x squared.

The inverse function, if you take f inverse of 4, f inverse of 4 is equal to 0.

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