Question

Find the inverse of f(x)=1 over x-2. I know you swap x and y to find your inverse but i think I'm going about it wrong.

Answer 1

show what you have so far

Answer 2

I'm getting f^-1(x)=x+2

Answer 3

I'll get you started

\[\large f(x) = \frac{1}{x-2}\]

\[\large y = \frac{1}{x-2}\]

\[\large x = \frac{1}{y-2}\]

\[\large x(y-2) = 1\]


The goal is to solve for y.

Answer 4

Sooo if i did my math correctly, is should be y=1/x+2?

Answer 5

let's finish up and find out

\[\large f(x) = \frac{1}{x-2}\]

\[\large y = \frac{1}{x-2}\]

\[\large x = \frac{1}{y-2}\]

\[\large x(y-2) = 1\]

\[\large xy-2x = 1\]

\[\large xy = 1+2x\]

\[\large y = \frac{1+2x}{x}\]

\[\large f^{-1}(x) = \frac{1+2x}{x}\]

Answer 6

You can rewrite the answer like this

\[\large f^{-1}(x) = \frac{1+2x}{x}\]

\[\large f^{-1}(x) = \frac{1}{x}+\frac{2x}{x}\]

\[\large f^{-1}(x) = \frac{1}{x}+2\]

Answer 7

so it looks like you got

\[\large f^{-1}(x) = \frac{1}{x}+2\]

Answer 8

Yay!!! :) your awesome ! Is it okay if you start me off on a similar one ?

Answer 9

sure, did you have one?

Answer 10

Yeah, its find the inverse of f(x)=2x-4.

Answer 11

When i first tried it i got y=x+4 over 2. Buut, im not so sure on it anymore.

Answer 12

\[\large f(x)=2x-4\]

\[\large y=2x-4\]

\[\large x=2y-4\]

\[\large x+4=2y\]

\[\large 2y=x+4\]

\[\large y=\frac{x+4}{2}\]

\[\large f^{-1}(x)=\frac{x+4}{2}\]

So you nailed it.

Answer 13

Thank you soo much !! It means alot :)

Answer 14

sure thing