Need a bit of help.

Question

Trying to find the image sets of two recipricol functions.

The first g(x)=1/(x-2)+5 (x not equal to 2)

The second g(x)=1/(x-2)+5 (x>2)

Now its quite easy to draw/sketch the graph but ive not really dealt with image sets of recipricol f functions before and so im getting a bit confused where to look.

I know the image set is the y axis and the domain is the x axis so...

am I right if I say

the first image set where x cant equal 2 is this:

[-∞,5)∪[5,∞)

and the second is where I get very lost.

From looking at the graph it seems that the image set is again
[5,∞)
When x > 2.

But it doesnt seem correct to me.