(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Graph f(x) = sqrt(x^2 - 2x), and find an interval on which it is one-to-one. Find the inverse of the function restricted to that interval.

2. Relevant equations

3. The attempt at a solution

What I can't do is really finding the inverse function. It seems very simple, but somehow I got stuck in the process.

swap x and y in the original function

y = sqrt(x^2-2x)

x = sqrt(y^2-2y)

and solve for y

so i did

x^2 = y^2-2y, and i tried to factor out y

x^2 = y(y-2)

x^2/y-2 = y

now i am really stuck. how can i pull that y out?

Thank you for any kind of help!!!

---- edited

I was thinking about this formula: d/dy f-1(x) = 1/ f ' (y)

i guess i can then integrate the d/dy f-1(x) and get f-1(x)?

so i started working again

f ' = (1/2 (x^2-2x) ^-1/2) * 2x-2

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

which is d/dy f-1

but the integration doesn't work!

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Find inverse function

**Physics Forums | Science Articles, Homework Help, Discussion**