Write the equation that results when you start with y = f(x), expand it vertically by a factor of 4, etc etc

Here is the full question:

Write the equation that results when you start with y = f(x), expand it vertically by a factor of 4, compress it horizontally by 1/2, translate it 2 units right and, 1 unit up and take its reciprocal.

If anyone could outline the steps taken to achieve the answer to this it would be much appreciated.

Thanks in advance.

y = f(x)
Expand it vertically by a factor of 4
y = 4f(x)
compress it horizontally by 1/2.
y = 4f(2x)
Translate it 2 units to the right
y = 4f(2(x-2)) = 4f(2x-4)
Translate it 1 unit up
y = 4f(2x-4)+1
Reciprocal
y = 1/[4f(2x-4)+1]