Question

find the inverse of the function
(in comments)

Answer 1

\[g(x)= \frac{ 4 }{ x+1 }+2\]

Answer 2

solve for x
x=(6-g)/(g-2)
that is inv of g(x)=6-x/x-2
asxis only a dummy variable to define the expression

Answer 3

interchage x and y

Answer 4

okay and then i subrtacted 2 from each side

Answer 5

\[y=\frac{ 4 }{ x+1 }+2\]
\[x=\frac{ 4 }{ y+1 }+2\]
then solve for y

Answer 6

\[x-2=\frac{ 4 }{ y+1 }\]
\[y=\frac{ 4 }{ x-2}-1\]

Answer 7

so far i got \[y+1=\frac{ 4 }{ x+2 }\] but i know it can be simplified more

Answer 8

*x-2

Answer 9

just subtract 1 both sides

Answer 10

whenever you have to solve for an inverse function or to check the function is onto solve for the basic variable
hence i solved and got the answer

Answer 11

so final answer is \[y=\frac{ 4 }{ x-2 }-1\] @jim_thompson5910

Answer 12

yes

Answer 13

divide the answer 6-x by x-2 you will get -1 as quottient and 4 as remainder which gives
-1+4/(x-2).the same asKatylon