Solve equation |f^-1(x)|= 1+f^-1(x)

Homework Statement

f(x) = (2x-3)/(x-1)
Solve the equation |f^-1(x)|= 1+f^-1(x)

Homework Equations

I'm pretty sure f^1(x) = (-3+x)/(x-2)

The Attempt at a Solution

I am not sure what solve means. Do i need to plug in values?

 

[Mark44]

Homework Statement

f(x) = (2x-3)/(x-1)
Solve the equation |f^-1(x)|= 1+f^-1(x)

Homework Equations

I'm pretty sure f^1(x) = (-3+x)/(x-2)

The Attempt at a Solution

I am not sure what solve means. Do i need to plug in values?

No, that wouldn't be very productive unless you just happened to pick a value that works.

I believe the problem is asking you to find the value of x that makes the equation a true statement.
Also, yes, the inverse is $f^{-1}(x) = \frac {x - 3} {x - 2}$
Replace $f^{-1}(x)$ by this expression in the equation you're given and get x all by itself.

 

[Ray Vickson]

Homework Statement

f(x) = (2x-3)/(x-1)
Solve the equation |f^-1(x)|= 1+f^-1(x)

Homework Equations

I'm pretty sure f^1(x) = (-3+x)/(x-2)

The Attempt at a Solution

I am not sure what solve means. Do i need to plug in values?

Make life easier for yourself by letting $f^{-1}(x) = y$, so your equation is $|y| = 1 + y$. First figure out the value of $y$, then figure out what must be $x$ to give you $f^{-1}(x) = y$.