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

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- Oct 15th 2009, 07:51 PMAsuhuman18finding the inverse of a function
Algebraically find the inverse function of f(x)=9-3e^x

- Oct 15th 2009, 07:58 PMsuperdude
to find the inverse you switch x and y, and then solve for y.

So do you know how to use ln's? - Oct 15th 2009, 08:08 PMAsuhuman18
no, could you please refresh my memory?

- Oct 15th 2009, 08:14 PMmr fantastic
- Oct 15th 2009, 08:16 PMmathaddict
- Oct 15th 2009, 08:19 PMAsuhuman18
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??? - Oct 15th 2009, 08:25 PMmr fantastic
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.

I advise dividing by 3 first. Then use the result I gave in my earlier reply. - Oct 15th 2009, 08:40 PMAsuhuman18
i dont know how thats the PROBLEM!!!!!! I dont get your theorem either i did what i thought you asked me to do

- Oct 15th 2009, 08:54 PMmr fantastic
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.