SOLUTION: Hello everyone, The question: Find the inverse of the function f(x) = {{{ sqrt (x^2 + (1/x^2)) }}} I am having trouble isolating the y for the inverse function. I would great

Question 105421: Hello everyone,
The question: Find the inverse of the function f(x) =
I am having trouble isolating the y for the inverse function. I would greatly appreciate any help. My work is shown below.
Thank you very much!
---
My work :
f(x) =
y =
x =
=

Answer by TP(29) (Show Source): You can put this solution on YOUR website!
Fine up to .
So we'll go from there.
x=
Square both sides:
.
Now multiply both sides by
We get:

Now subtract from both sides:
We get (i)
Let and (i) becomes:

Now using the formula for the solution of i.e.
where , and
we get:

But and so:

Hence .
Now there are TWO possible answers for the solution to the equation but only ONE is correct for the inverse function and it is:
ANS.
(NB. I'll leave it up to you to work out what represents.
You should also use your calculator to check the inverse function answer - I suggest, for example, that you replace x by 4 or a similar small value).

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