Question

what is the inverse of f(x)=(x+3)/(x-2)

Answer 1

Switch Xs and Ys

Answer 2

Then solve for y

Answer 3

i just want to check because my math books syas the anser is (2x+3)/(x-1)

Answer 4

but, on the last problem, my book had a mistake so now i dont trust it

Answer 5

\[y=\frac{x+3}{x-2}\]
\[y(x-2)=x+3\]
\[yx-2y=x+3\]
\[yx-x=3+2y\]
\[x(y-1)=3+2y\]
\[\frac{x(y-1)}{y-1}=\frac{3+2y}{y-1}\]
\[x=\frac{3+2y}{y-1}\]
now just interchange y with x
and x with f^(-1)(x)

Answer 6

could you also check what the inverse for this one is f(x)=x^3+1. My books says the anser is \[5\sqrt{x-1}\]

Answer 7

just solve for x and replace x with f^(-1)(x) and replace y with x

let me see your attempt

Answer 8

well i got and everyone else is telling me that the answer is \[\sqrt[3]{x-1}\]

Answer 9

you have
\[y=x^3+1\]
how are we gonna solve this for x?

Answer 10

we first subtract 1 from both sides, then cub root both sides

Answer 11

right so after subtracting one on both sides we get:
\[y-1=x^3\]
then take cube root of both sides
\[\sqrt[3]{y-1}=x\]
now replace y with x and x with f^(-1)(x)

Answer 12

alright, guess my book has a mistake

Answer 13

yes