Should I install DirectX 9.0(c) on my Windows 7 RTM machine?

I've just installed a new game on my Windows 7 RTM machine. The game is asking me to install DirectX 9.0(c). I said 'NO' because my machine has DirectX 11 (confirmed with dxdiag). When I run the game, an error occurs informing me that d3dx9_39.dll is missing.

Is Windows 7 DirectX backwards-compatible?

Yes.

The Direct X installer is smart enough to just pop files there for stuff to work. Some programs go about things the wrong way (as is the case here) and ask for files directly, rather than the functionality the files provide.

You can safely allow modern games to install whatever version of DirectX they need. Doing so will NOT affect the DirectX that is currently installed on your computer.

As you have seen, not allowing a game to install its required version of DirectX might result in the game not working.

There is one great way to do this if you do not want to install previous versions of DirectX: get the required .dll file (from the Internet or from a system where that version of DirectX is installed) and place it in the root folder of the application looking for that file.

This will work fine.