# Thread: finding the inverse of a function

1. ## finding the inverse of a function

Algebraically find the inverse function of f(x)=9-3e^x

2. to find the inverse you switch x and y, and then solve for y.
So do you know how to use ln's?

3. no, could you please refresh my memory?

4. Originally Posted by Asuhuman18
no, could you please refresh my memory?
Use the fact that if $\displaystyle A = B^C$ then $\displaystyle C = \log_B A$. Please show what you've tried and say where you get stuck.

5. Originally Posted by Asuhuman18
Algebraically find the inverse function of f(x)=9-3e^x
HI

let $\displaystyle f^{-1}x=y$

$\displaystyle x=f(y)$

$\displaystyle x=9-3e^y$

$\displaystyle 3e^y=9-x$

Then apply take the log of both sides to the base e .

6. so would it be f(x)=9-3e^x
= ln(y)= ln(9)-3*ln(e^x)
= ln(y)= ln(9)-3x
this is where i get stuck if this is even right. I try to solve for x which would be (ln(y)-ln(9))/3=x right???

7. Originally Posted by Asuhuman18
so would it be f(x)=9-3e^x
= ln(y)= ln(9)-3*ln(e^x)
= ln(y)= ln(9)-3x
this is where i get stuck if this is even right. I try to solve for x which would be (ln(y)-ln(9))/3=x right???
No. Please show every single step, starting from where you swap y and x. And please show how you used the crucial fact I mentioned in my earlier reply.

HI

let $\displaystyle f^{-1}x=y$

$\displaystyle x=f(y)$

$\displaystyle x=9-3e^y$

$\displaystyle 3e^y=9-x$

Then apply take the log of both sides to the base e .
I advise dividing by 3 first. Then use the result I gave in my earlier reply.

8. i dont know how thats the PROBLEM!!!!!! I dont get your theorem either i did what i thought you asked me to do

9. Originally Posted by Asuhuman18
i dont know how thats the PROBLEM!!!!!! I dont get your theorem either i did what i thought you asked me to do
If you don't understand the rule I posted then you're strongly advised to go back a step and thoroughly review exponentials and logarithms before continuing with this problem. Understanding the relationship between them is crucial to understanding how to solve the problem you posted.