Question

If f(x) = log3 x, find f ^(- 1)(x).

Answer 1

Do you know how to find the inverse of a function?

Answer 2

No.. I know its asking for the inverse, but not how to find it. Do you replace f(x) with y and then switch x and y and then solve for y ? Maybe not ..

Answer 3

Step 1: rewrite y = f(x)
Step 2: interchange x and y
Step 3: solve for y
Step 4: \[f ^{-1}=...\]Do you understand?

Answer 4

Oh okay, yes. That's what I thought, but then I thought that may not apply to this ? But I see. Thanks!

Answer 5

Step 1:\[y =\log_{3}x \]Now can you do the rest?

Answer 6

then it would be x=log3y. then that makes 3^y right ?

Answer 7

Right!\[x =\log_{3}y \]Now can you do the next step?

Answer 8

Hint: The inverse of a logarithmic function is an exponential function.

Answer 9

yeah, so wouldn't that make it y=3^x ?

Answer 10

Excellent! \[∴ f ^{-1}(x)=3^{x}\]

Answer 11

Yay ! Thanks for helping :)

Answer 12

Are you good now?

Answer 13

Great!

Answer 14

yes!

Answer 15

I have to log out now if there's nothing else. Bye!