Question

if f(x) =x-1/x=1 then f^-1(x)=

Answer 1

\[f(x)=\frac{x+1}{x-1}\]?

Answer 2

@Haseeb96

Answer 3

and you want the inverse right?

Answer 4

yeh @satellite73

Answer 5

usual method is to write
\[x=\frac{y+1}{y-1}\] and solve for \(y\)

Answer 6

x-1/x+1 yeh

Answer 7

takes a few steps to do it

Answer 8

ok

Answer 9

oh let me get it right
\[f(x)=\frac{x-1}{x+1}\] is the original function yes?

Answer 10

yes

Answer 11

not the one i wrote above'
ok we start with \[x=\frac{y-1}{y+1}\] and solve for \(y\)

Answer 12

first step is to multiply by \(y+1\) to get rid of the fraction and write \[x(y+1)=y-1\]

Answer 13

then?

Answer 14

next step is to distribute
\[xy+x=y-1\]

Answer 15

then since you want \(y\) by itself, you have to put it on one side of the equal sign
say the left, by writing
\[xy+x-y=-1\] then put the \(x\) on the right via
\[xy-y=-1-x\]

Answer 16

finally factor the \(y\) out of the left hand side, so you know what to divide by
\[y(x-1)=-1-x\]

Answer 17

and then divide to get \[y=\frac{-1-x}{x-1}\]

Answer 18

now there are way to many minus signs, so it might be nice to clean it up and have
\[f^{-1}(x)=\frac{x+1}{1-x}\]

Answer 19

i don't think i skipped any steps
if any are not clear let me know

Answer 20

no its clear thanks:)

Answer 21

yw

Answer 22

one thing what about the minus sign?

Answer 23

when we solved, the answer was ugly, it was
\[\frac{-1-x}{x-1}\]

Answer 24

there is really nothing wrong with that, but it has a lot of minus signs in it
if you multiply the top and bottom by \(-1\) i.e. change all the signs, you get the nicer looking
\[\frac{x+1}{1-x}\]

Answer 25

i.e. \[\frac{-1-x}{x-1}\times \frac{-1}{-1}=\frac{x+1}{1-x}\]

Answer 26

ok thanks now got that

Answer 27

yw again