# finding the inverse of a function

• Oct 15th 2009, 07:51 PM
Asuhuman18
finding the inverse of a function
Algebraically find the inverse function of f(x)=9-3e^x
• Oct 15th 2009, 07:58 PM
superdude
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 PM
Asuhuman18
no, could you please refresh my memory?
• Oct 15th 2009, 08:14 PM
mr fantastic
Quote:

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.
• Oct 15th 2009, 08:16 PM
Quote:

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 .
• Oct 15th 2009, 08:19 PM
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???
• Oct 15th 2009, 08:25 PM
mr fantastic
Quote:

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.

Quote:

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.
• Oct 15th 2009, 08:40 PM
Asuhuman18
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 PM
mr fantastic
Quote:

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.