## anonymous one year ago f(x) = 2e^3x + 1 Find the inverse f^-1(x). Can anyone help?

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1. jackellyn

Set it equal to y. Switch the x and the y, solve for y.

2. jackellyn

y=2x^3+1 x=2y^3+1 Solve for y.

3. anonymous

thx @jackellyn

4. jackellyn

5. anonymous

my calculator is messing up, can you walk me through it pls. @jackellyn

6. jackellyn

so to solve for y you need to perform reverse operations. If we have x=2e^3y +1 What do we need to do first to get y alone?

7. anonymous

subtract 3y on both sides @jackellyn i think

8. jackellyn

Well the 3y is part of the exponent so we can't get rid of it just yet. First we need to get rid of the +1 and move it to the other side so do we add it to both sides or subtract it?

9. anonymous

subtract it @jackellyn

10. jackellyn

Right so we have x-1= 2e^3y Now we need to get rid of the 2 in front of the e^3y. What do you get?

11. anonymous

divided

12. anonymous

@jakellyn if thats correct

13. anonymous

@jackellyn you there

14. jackellyn

Yes, divide so then we have (x-1)/2=e^3y Do you remember the opposite operation of e?

15. anonymous

I don't recall @jackellyn

16. jackellyn

You need to take the natural log of both sides to get rid of the e and stay only with 3y. ln (x-1/2)=ln e^3y ln (x-1/2)=3y Solve for y.

17. anonymous

$y =\frac{ x }{ 3}-\frac{ 1 }{ 6 }$ is that correct? @jackellyn

18. anonymous

so is this the inverse for $f ^{-1}$

19. anonymous

@jackellyn idk if you saw my replies^^^^

20. jackellyn

Sorry, I didnt. You can't get rid of the ln. It stays all together and then you can divide the 3. So $y=\frac{(\ln \frac{ x-1 }{ 2 }) }{ 3 }$

21. anonymous

so thats the inverse of $f ^{-1}(x)$

22. jackellyn

It is the inverse of f(x). $f ^{-1}(x)$ is the notation for inverse.

23. anonymous

okay i understand now thx a lot

24. anonymous

@jackellyn one more question what is the inverse