Question

What is the inverse function of f(x)=x over x+1 . sorry , i dont know how to make the fraction sign .

Answer 1

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

Answer 2

set
\[x=\frac{y}{y+1}\] and solve the equation for \(y\)
that will be your inverse

Answer 3

any idea how to do that?

Answer 4

not a clue

Answer 5

first get rid of the fraction by multiplying both sides by \(y+1\) to get
\[x(y+1)=y\]

Answer 6

then multiply out on the left to get
\[xy+x=y\]

Answer 7

put all the \(y\) terms on one side by subtracting \(xy\) and get
\[x=y-xy\]

Answer 8

factor out the \(y\)
\[x=y(1-x)\]

Answer 9

divide both sides by \(1-x\) and finish with
\[y=\frac{x}{1-x}\] and that is your inverse

Answer 10

thank you ;)

Answer 11

yw
hope it is clear, all steps are there