MAIN CONCEPTS
In dealing with functions that do not take the regular form , we employ a technique called switching the variable.
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Unlike the more usual functions that take the form  an expression in terms of x, this function we are dealing with takes the form . While a little intimidating, you should be able to solve it quite easily with a solid foundation on definitions.

Our goal is to find , so if we could somehow pick a certain expression and substitute it into  and then get , we are on our way because we simply substitute that same expression into . However, the problem lies in finding that expression.

To efficiently solve this problem, we use a technique called ‘the switching of variable’, commonly used in other areas of algebra. We introduce a new variable to simplify the functional relationship to the point where we can immediately put  into the function much like how we put a value of x into the function .

Let  and solve for x in terms of y. When  and  we have

Solving for x in terms of y gives

with the imposed condition that . We can now substitute both equations of x and y into the function.

We have simplified the functional relationship so now we can immediately let , for , giving us

which is the answer.