I need to know that my amd radeon hd 8730m GC is activated and working or not.

Yes, AMD Radeon HD 8730m is present and working. With second generation and above Intel Core i series of processors, Intel introduces its graphics processor in the main processor (known as embedded graphics processor), hence computers equipped with such processors, with AMD or nVidia graphics card (known as discrete graphics processor/card), shows two different devices under Display adapters. Embbeded graphics card is for low performance graphics like Windows Aero effects. Discrete graphics card is for complex applications like games or CAD software.

With this scenario, a technology, Switchable Graphics, is available that allows you to switch between low performance and high performance graphics seamlessly. The following screenshots will be helpful:

Go to Desktop -> right click anywhere in plain area. You can see a menu like below:

Click on Configure Switchable Graphics. You can see a dialog like below:

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Now, for any of the application you want to change the performance, select it -> click on the down arrow under Graphics Setting -> select High Performance (to use AMD graphics) or Low Performance (to use Intel graphics). Then click Apply to use the settings.

Kindly install AMD Catalyst from the following link:

http://support.amd.com/en-us/download

Select your model to download the AMD Catalyst drivers software. Install the drivers, restart the PC and the check. Kindly do not download beta releases as it is in test stage.