Question

f(x)=1-x/3x+2. Find f^-1(x)

Answer 1

\[x=\frac{1-y}{3y+2}\] solve for \(y\) it takes a few steps

Answer 2

Can you type out the steps?

Answer 3

1) multiply both sides by \(3y+2\) to get \[x(3y+2)=1-y\]

Answer 4

2) distribute on the left to get
\[3xy+2x=1-y\]

Answer 5

3) put all terms with \(y\) on one side, all else on the other
\[3xy+y=1-2x\]

Answer 6

4) factor out the \(y\) on the left
\[(3x+1)y=1-2x\]

Answer 7

5) divide both sides by \(3x+1\)
\[y=\frac{1-2x}{3x+1}\]

Answer 8

6) write
\[f^{-1}(x)=\frac{1-2x}{3x+1}\]

Answer 9

THANKS!

Answer 10

it was a lot of steps
check my algebra, but i think it is right
yw

Answer 11

It's correct.