Q: My engine rpm go way up win i start car stay up for 30 to 40 seconds on 2004 Cadillac SRX

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Before coming down so I can start car
(1) Answer
This sounds the most like a vacuum leak. If your engine is sucking in more air than it should, especially if that air is coming from somewhere besides through the air filter, you will find this condition.
If it acts normal when it heats up, likely you have intake manifold gasket issues, but it really could be a long list of "maybes".

Do you have a check engine light coming on? If so, scan and post the trouble codes here.