Are oil and the US Dollar inverse to each other? No. At least not always.
There are numerous articles out about "Dollar Up & Oil Down", or "Dollar Down & Oil Up".
Sometimes that inverse movement occurs, and sometimes it does not. When the inverse correlation is working, there may be a trade, but when it is not, find something else to do.
Here is an 18-year monthly chart comparing the US Dollar (proxy UUP) to West Texas Intermediate Crude (proxy USO). You can see inverse correlation sometimes and not at other times.
The red line is for the US Dollar Index (USD against a trade weighted basket of currencies). The black line is the spot price of crude.
There is substantial argument today that the Dollar will fall due to all of the debt issuance associated with the economic rescue programs. There are also strong voices saying that oil will rebound to perhaps $70+ when economies improve, based on the average deep sea finding and lifting cost. That would suggest an inverse chart correlation may exist in the future, but the causation is not described as the same for each. Any future correlation may be partly coincidental and partly cause and effect.
It is not safe to assume that if one rises the other will necessarily fall. You must stay on your toes, or lose your toes, and maybe some fingers too. Remember that a big part of making money, is not losing money. Acting on false assumption about structural price relationships is one good way to lose money.