Question

Will give medal!

Answer 1

If \[ f(x) = \log_{3} (x + 1)\] What is \[f ^{-1}(7)\]

Answer 2

To find the inverse:

Replace f(x) with y
Switch x's and y's, so put x where y is and x where y is.
Solve for y
Replace y with f^-1(x)

Answer 3

There aren't any Y's... ._. you mean the f(x)?

Answer 4

Read the first line of finding the inverse :p

Answer 5

How on earth did I miss that .-.

Answer 6

^.^

Answer 7

I'm stuck on solving for y

Answer 8

\[
x =f^{-1}(f(x)) = \log_3(f^{-1}(x)+1)
\]In this case, let \(x=7\) and we get: \[
7 = \log_3(f^{-1}(7)+1)
\]At this point, we solve for \(f^{-1}(7)\).

Answer 9

\[
3^7 = f^{-1}(7)+1
\]

Answer 10

Wait but how on earth did you get to that equation in the first place??!?

Answer 11

Which one?

Answer 12

The first one

Answer 13

You mean \(x=f^{-1}(f(x))\)?

Answer 14

He did the same thing as I explained he used the actual notation instead of y and then switching to f^-1(x) .

Answer 15

instead*

Answer 16

He only steps I read that lead me to writing an equation came out to x-log3(y+1) I had no idea how to solve that, and I have no idea how he got to that equation.

Answer 17

The*

Answer 18

So right now the only equation I have to do anything with is x-log3(y+t) I have no idea how the one you mentioned was made. I don't know what law or rule it was, I have no idea.

Answer 19

Let's do this again: \[
x=f^{-1}(f(x))
\]This is a basically a definition of the inverse function.
Let \(f(x) = 7\).

The result: \[
x = f^{-1}(7)
\]This means that if we let \(f(x) = 7\) then that means \(x = f^{-1}(7)\).

So start with our original function equation: \[
f(x) = \log_4(x+1)
\]Now let \(f(x) = 7\) and \(x=f^{-1}(7)\): \[
7 = \log_3(f^{-1}(7)+1)
\]

Answer 20

The only thing to be careful of is the assumption that there is some \(x\) where \(f(x)=7\). It might not actually exist, in which case this methodology could lead to incorrect answers.

Answer 21

I'm trying very hard to understand this, I'm looking at the equation, heck just the first equation. I have no idea what you were talking about with an inverse function, and how you got that from the original equation. I'm starting to think that I'm possibly just lacking the knowledge to understand this.

Answer 22

When you have a question that says f^-1 thats asking you to find the inverse of a function, have you covered this in your class yet?

Answer 23

I'm not sure. I do remember the whole y=b^x is equivalent to logb(y)=x

Answer 24

Here give this a read, it will tell you what an inverse function is! http://www.mathsisfun.com/sets/function-inverse.html

Answer 25

http://www.mathwords.com/l/logarithm_rules.htm LOGARITHM RULES

Answer 26

I honestly don't remember covering this in my course.

Answer 27

Consider: \[
\color{red}{y} = \log_{\color{blue}{b}}(\color{green}{x}) \iff \color{blue}{b}^{\color{red}y}=\color{green}{x}
\]
Same applies here:
\[
\color{red}7 = \log_{\color{blue}3}(\color{green}{x+1}) \iff \color{blue}3^{\color{red}7}=\color{green}{x+1}
\]

Answer 28

I understand that, I get that much I think.

Answer 29

@freflex nice profile pic