Question

find the inverse of f(x) = 1-x / x

Answer 1

You can find the inverse like this:
\[y=\frac{1-x}{x}\]\[xy=1-x\]\[xy+x=1\]\[x(y+1)=1\]\[x=\frac{1}{1+y}\]

Answer 2

Now just replace y with x to get:
\[f^{-1}(x)=\frac{1}{1+x}\]

Answer 3

pls show the verification f(f^-1(x)) @bahrom7893

Answer 4

To verify we need to confirm that \[f(f^{-1}(x))=1\]

Answer 5

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

Answer 6

Do the algebra and confirm that it eventually equals 1.

Answer 7

ty