Grade 12 Math (inverse of functions)

[Ethan_Tab]

f(x)=[((x-1)/(x+1))+((x-1)/(x+1))]^1/2

What is F^-1(x)

No matter what I try I am unable to isolate for y after switching x's with y's. Any ideas?

 

[Mark44]

f(x)=[((x-1)/(x+1))+((x-1)/(x+1))]^1/2

The innermost expression is $\frac{x - 1}{x + 1} + \frac{x - 1}{x + 1}$, which can be simplified. Is that what you meant to write?

What is F^-1(x)

No matter what I try I am unable to isolate for y after switching x's with y's. Any ideas?

BTW, this looks like a homework problem, so I'm moving this thread.

 

[RUber]

This is a pretty common problem. I'll work on a similar one as an example.
$y = \sqrt{ \frac{x-1}{x+1} }$
$y^2 = \frac{x-1}{x+1},\, y\geq 0$
$y^2 = \frac{x+1}{x+1}-\frac{2}{x+1}$
$y^2-1 = -\frac{2}{x+1}$
$x+1 = -\frac{2}{y^2-1}$
$x= -\frac{2}{y^2-1}-1=-\frac{2}{y^2-1}-\frac{y^2-1}{y^2-1}=-\frac{y^2+1}{y^2-1}$