Question

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

Answer 1

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

Answer 2

y=2x^3+1
x=2y^3+1

Solve for y.

Answer 3

thx @jackellyn

Answer 4

Did you get the answer?

Answer 5

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

Answer 6

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?

Answer 7

subtract 3y on both sides @jackellyn i think

Answer 8

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?

Answer 9

subtract it @jackellyn

Answer 10

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?

Answer 11

divided

Answer 12

@jakellyn if thats correct

Answer 13

@jackellyn you there

Answer 14

Yes, divide so then we have

(x-1)/2=e^3y

Do you remember the opposite operation of e?

Answer 15

I don't recall @jackellyn

Answer 16

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.

Answer 17

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

Answer 18

so is this the inverse for \[f ^{-1}\]

Answer 19

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

Answer 20

Sorry, I didnt. You can't get rid of the ln. It stays all together and then you can divide the 3.

So \[y=\frac{(\ln \frac{ x-1 }{ 2 }) }{ 3 }\]

Answer 21

so thats the inverse of \[f ^{-1}(x)\]

Answer 22

It is the inverse of f(x).

\[f ^{-1}(x)\] is the notation for inverse.

Answer 23

okay i understand now thx a lot

Answer 24

@jackellyn one more question what is the inverse