The inverse of a function?

Question

I had a little trouble with this...

Normally, to find the inverse of a function, say, f(x) = 2x-1:

y = 2x -1

And then just switch the domain and range and solve for y, right?

x = 2y - 1

y = (x + 1) / 2

But what if f(x) = 1/x?

By that,

y = 1 / x

x = 1/ y

and solving for y,

You get 1 / x.

So is the inverse of 1/x just 1/x?

Answer 1

You are correct.  The inverse of a function reflects itself over the line y = x.  If you graph y = 1/x you will see that it is symmetric over the line y = x, thus it is its inverse.

Answer 2

you got it quite right

Answer 3

Yes, you are right, if you were to actually graph this, you would be able to see it.