Question

what is the inverse of the function f(x)=x/(x+3)

Answer 1

solve for x

Answer 2

in terms of f(x)

Answer 3

Let y = f(x)

\[y = \frac{x}{x+3}\]

Then swap x and y:

\[x = \frac{y}{y+3}\]

Then isolate y

Answer 4

change f(x) by x and x by f(x)

Answer 5

Finally after isolating y, replace it with \[f^{-1}(x)\]

Answer 6

I tried that and ended up with \[y=xy+3x\] and i dont know where to go from there

Answer 7

\(y - xy = 3x\)
\(y(1-x) = 3x\)
\[y = \frac{3x}{1-x}\]

Answer 8

Ah thanks! I get it, you have to pull out a factor

Answer 9

\[f^{-1}(x) = \frac{3x}{1-x}\]