Is the reciprocal of f (x) = (2x+1) / (x-3) -> F^-1 (x) = (3x+1) / (x-2) ?

I don't have access to a teacher in the present moment, I just want to make sure I understand right. If I am wrong please point out where is my error, thank you.

f (x) = (2x+1) / (x-3)

y=(2x+1) / (x-3)

x=(2y+1) / (y-3)

x(y-3)=(2y+1)

xy-3x-2y=1

xy-2y=(3x+1)

y(x-2)=(3x+1)

y(x-2)/(x-2)=(3x+1)/(x-2)

y=(3x+1)/(x-2)

Re: Is the reciprocal of f (x) = (2x+1) / (x-3) -> F^-1 (x) = (3x+1) / (x-2) ?

Hello, letranger9000!

You don't mean "reciprocal" . . . You mean "inverse".

Good work!

Punchline: /

Do you know how to check your answer?

Evaluate or .

Either must simplify to

Multiply by

ta-*DAA!*

Re: Is the reciprocal of f (x) = (2x+1) / (x-3) -> F^-1 (x) = (3x+1) / (x-2) ?

Be careful of your terminolgy. The **reciprocal** of is .

But the **inverse** function is as you have.

Re: Is the reciprocal of f (x) = (2x+1) / (x-3) -> F^-1 (x) = (3x+1) / (x-2) ?

Thanks guys, appreciated. And yes I meant inverse, although in french an "inverse" is a "reciprocal", hence the source of my confusion.