Question

is y=x-9 an inversed function

Answer 1

To check, translate y into x and x into y, like this
$$
x=y-9
$$
Now solve for y:
$$
y=x+9
$$
If it is an inverse function then taking this function plugging in y=x-9 for x should get you back to x:
$$
y=x+9\\
y=(x-9)+9\\
=x
$$
Since the inverse function of y=x-9 gave us back x, then it is an inverse function of y=x+9.
Notice that we can do the reverse. Plug in y=x+9 into your original equation and you should get back x:
$$
y=x-9\\
=(x+9)-9\\
=x
$$
Which shows that y=x-9 is the inverse function of y=x+9.

Essentially ones takes you from the x domain the to y domain. The other takes you back to the x domain and gives you back what you started with, namely x.

Hope this helps.

Answer 2

It did thanks