Question

Suppose f(x) = (2x+1)/(3x-1). Let g(x) be the inverse of f. Find g(x).

Answer 1

My work so far:

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

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

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

^ This is where I get stuck. Am I even on the right track here?

Answer 2

f(g(x)) = x

Answer 3

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

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

3xg(x) - x = 2g(x)+1

combine like points and get g(x) all by its little lonesome

Answer 4

Oh, ok. That's a little different then how I remembered it. What level of math would you say this question is?

Answer 5

intermediate algebra lvl

3xg(x) - x = 2g(x) + 1
-2g(x) + x -2g(x) +x
--------------------
3xg(x)-2g(x) = x + 1

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

Answer 6

in your steps, you just gotta keep in mind that you want to gather all your "y" parts to one side to factor out the "y" and move the rest of it to the other side

Answer 7

But I wonder, it doesn't really say that g = x, just that g(x) is the "inverse" of f. So basically g(x) is f^1(x). Right?

Answer 8

^-1, yes

but an inverse has the property that if g(x) is the inverse of f(x) then: f(g(x)) = x

Answer 9

Ah. Ok thanks then. I don't have the possible answers in front of me, but I will give that a try next time.

Answer 10

good luck ;)