## anonymous 3 years ago What is the inverse of the function f(x)=1/3x-2?

1. anonymous

y=(1/3)x-2 Switch y&x and solve x=(1/3)y-2

2. anonymous

So what is the next step you would do?

3. anonymous

idk

4. anonymous

So we want to get y by itself. Lets add 2 to each side.

5. anonymous

$x+2 = \frac{ 1 }{ 3 }y$

6. anonymous

Does that make sense?

7. anonymous

So how will we now "move" the 1/3?

8. anonymous

Okay. f(x)=1/3x-2 Take f(x) = y y = 1/(3x - 2) y*(3x - 2) = 1 3xy - 2y = 1 -1 - 2y= - 3xy -(1 + 2y) = -3xy 1 + 2y = 3xy (1 + 2y)/y = 3x (1 + 2y)/3y = x Lastly, replace y with x, we have: (1 + 2x)/3x = y Which is the inverse.

9. anonymous

Wait, is it $F(x) = \frac{ 1 }{ 3x - 2 }?$

10. anonymous

Or is it $F(x) = \frac{ 1 }{ 3 }x - 2?$

11. anonymous

Wouldn't it be 3(x+2)=y y=3x+6 $f ^{-1}(x) = 3x+6$

12. anonymous

thats what i got but i got -3x but i see what i did wrong, thank you

13. anonymous

Thank you.