need quick question answered

If f(x) = log3 (x + 1), what is f−1(2)?

1

8

10

27

Question

need quick question answered

If f(x) = log3 (x + 1), what is f−1(2)? 

 1 

 8 

 10 

 27

gavin39 · Answer

I give medals and fan

hero · Answer

$f(x) = log_3(x + 1)$

Let y = f(x)

$y = log_3(x + 1)$

Swap x and y:
$x = log_3(y + 1)$
Apply the "relationship" rule for logs and exponents:

$3^x = y + 1$

Subtract 1 from both sides:
$3^x - 1 = y$

Replace y with $f^{-1}(x)$
$3^x - 1 = f^{-1}(x)$

Rewrite as

$f^{-1}(x) = 3^x - 1$

Can you now try evaluating $f^{-1}(2)$?

gavin39 · Answer

in all honesty I cant because I know nothing about this stuff. Confuses me bady

hero · Answer

I see...

gavin39 · Answer

O wait I got it. Its 8

hero · Answer

Yes, but now, try to understand the entire process.

gavin39 · Answer

yeah I need to study hard on it

hero · Answer

There are only a few things that might trip you up:

1. Replacing f(x) with y
2. Swapping x and y
3. Applying the relationship rule for logs and exponents. 
4. Isolating y
5. Replacing y with f^{-1}(x)

Anytime you have to find the inverse of a function, you'll have to do such things.

hero · Answer

Step 3 will be applied at certain points when dealing with finding the inverse of logs or exponents. All the other steps are general when finding the inverse of any function with x and y as variables.