find the inverse of the function
(in comments)

Question

find the inverse of the function
(in comments)

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

interchage x and y

anonymous · Answer

okay and then i subrtacted 2 from each side

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

*x-2

anonymous · Answer

just subtract 1 both sides

anonymous · Answer

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

anonymous · Answer

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

anonymous · Answer

yes

anonymous · Answer

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