What you're looking at is known as "the transformation theorem" and is just an integral change of variables written in probability notation.

Suppose g is an increasing function and Y = g(X). Then

```
F_Y(y) = P( g(X) < y ) = P( X < g^{-1}(y) ) = F_X( g^{-1}(y) )
```

To obtain the PDF, differentiate both sides of the equation above:

```
f_Y(y) = f_X( g^{-1}(y) ) D_y ( g^{-1}(y) )
```

where D_y means derivative with respect to y. Now if g were a decreasing function we'd have

```
F_Y(y) = P( g(X) < y ) = P( X > g^{-1}(y) ) = 1 - F_X( g^{-1}(y) )
```

and

```
f_Y(y) = f_X( g^{-1}(y) ) | D_y ( g^{-1}(y) ) |.
```

In the last line we would have -D_y. Since g is a decreasing function, it's derivative is negative and so the absolute values take care of the negative sign.