How can I make the edges of an image fade/feather along the edges?

I have taken my image and duplicated it. Then Selected one and applied blur I then aligned both images with non-blurred on top and did Object>Clip>Set. Both images vanish

I have also converted to path, duplicated, then selected one path and applied blur. I then selected both images and did Extensions>Generate from path>Interpolate (with interpolate style selected). Nothing happened. 

What am I doing wrong, that the blurred image is not cutting out and leaving the image with blurred lines?

Maybe a mask?

As TD says, a mask is the way to go. I find that it is slightly easier to work with if you first group the image, then apply a mask to the group. This allows you to double-click to enter the group and adjust the position of the image, without having to release and re-set the mask.

There are more details about masking, and about the group-before-masking technique in parts 14 and 32 of my tutorial series in Full Circle Magazine (free download): https://inkscape.org/forums/tutorials/inkscape-tutorials-in-full-circle-magazine/

Thank you so much. I am trying this, However, the whole circle is blurring, not giving me an edge blurred and selected area clear. 

Alright, I read the article. The picture I am trying to use, is not a group (yet) does this matter?

Maryalicia

Alright, I read the article. The picture I am trying to use, is not a group (yet) does this matter?

No, masking works quite happily on individual objects. The reason for suggesting a group is that it lets you reposition the image within the masked area without having to release and re-set the mask. This assumes that your use of the word 'picture' implies a bitmap image - if you actually mean several separate objects making up a drawing in Inkscape then you would need to group them first.

Assuming you're working with a bitmap image, the workflow without a group is as follows (as shown in TD's animation):

1. Import your image into Inkscape.
2. Draw a mask on top of the image. The fill must be 100% white. In TD's example it's an ellipse.
3. Blur the mask.
4. Select both the mask and the image.
5. Object > Mask > Set.

If you need to reposition the image within the masked area you'll have to use Object > Mask > Release, then repeat steps 4 & 5 above. Grouping avoids this:

1. Import your image into Inkscape.
2. Put your image into a group. It doesn't matter that it's the only thing in there.
3. Draw a mask on top of the group. The fill must be 100% white. In TD's example it's an ellipse.
4. Blur the mask.
5. Select both the mask and the group.
6. Object > Mask > Set.

Note that there's an extra step 2. Now if you need to reposition the image you can double-click on it to enter the group, then move the image around within the mask, before double-clicking on the background canvas to exit the group.

If this doesn't clear things up, it would be helpful if you could upload your SVG file so that we can understand your description in context.