What is the Correct Method for Finding the Inverse of a Function?

[the_awesome]

Homework Statement

It says to find the inverse of a function. I can figure out the answer of x by guessing, but its best to show a good way of working out :P also note that my calculator cannot do the log to a base part correctly.

All i want to know is if I've done it correctly. don't try to over complicate it for me :P I am pretty stupid and in grade 12 lol

Homework Equations

Find the inverse of:
6^6x-2 = 81

The Attempt at a Solution

6^6x-2 = 81
6^6y-2 = x + 81
6y-2 = log₆(x+81)
6y = log₆(x+81) + 2
y = log₆(x+81) + 2 <<<<<<< this means all of this divided by 6
--------------------------
6


from recalling what someone said to me, they had a solution that was something like:

log₆
--------------- +2
log₈₁
_________________________________ <<<<< divide whole thing by 6
6



which is correct? is my attemp any good?

 

[Mark44]

Homework Statement

It says to find the inverse of a function. I can figure out the answer of x by guessing, but its best to show a good way of working out :P also note that my calculator cannot do the log to a base part correctly.

All i want to know is if I've done it correctly. don't try to over complicate it for me :P I am pretty stupid and in grade 12 lol

Homework Equations

Find the inverse of:
6^6x-2 = 81

Your problem, as stated, doesn't make any sense. You can't find the inverse of an equation. You can solve an equation, and in this case, you can solve for x in the equation.

The Attempt at a Solution

6^6x-2 = 81
6^6y-2 = x + 81

Where did the x on the right side come from? You can't just stick an x in somewhere. And x in the first equation miraculously turned into y. I understand why you did this, since you thought you were finding an inverse, and your teacher has burned into your mind the idea that you have to switch the x and y. In this context, and as already mentioned, your job isn't to find an inverse.

6y-2 = log₆(x+81)
6y = log₆(x+81) + 2
y = log₆(x+81) + 2 <<<<<<< this means all of this divided by 6
--------------------------
6


from recalling what someone said to me, they had a solution that was something like:

log₆
--------------- +2
log₈₁
_________________________________ <<<<< divide whole thing by 6
6



which is correct? is my attemp any good?

Well, neither is correct, but I think you are misremembering what your friend told you.

First off, this problem has nothing to do with finding the inverse of anything, so put that thought out of your mind. I think that if you go back and look at how the problem is stated, it will say something like this:

Solve for x in the equation 6^6x-2 = 81.

If you take the log of both sides, you get this:
(6x - 2) log(6) = log(81)

Now, can you solve this equation for x?

 

[tnutty]

Yep pretty much what Mark said. y is not a function of x, so you can't find the inverse.
from your equation, you can
solve for x so the left side equals the right side, which is 81 by taking ln() of both sides.
But you cannot find the inverse of that equation because its not a function

 

[xaos]

looks like your friend simply solved for x using base 10. your attempt is using base 6 (with the error of putting in a magical variable y). I'm making a leap by ignoring some mistakes.

 

[the_awesome]

If you take the log of both sides, you get this:
(6x - 2) log(6) = log(81)

Now, can you solve this equation for x?

actually, my friends solution was nearly spot on.

x = (log(81) divided by log(6) + 2) divide this whole thing by 6
x = 0.74

thanx for ur help :) but looking at what my friend said, it was pretty dam close. (too bad my memory sucks, haha)

 

[Mark44]

That might be, but what he had and what you wrote are different, I think.