Question

What is the inverse of the function f(x)=1/3x-2?

Answer 1

y=(1/3)x-2
Switch y&x and solve

x=(1/3)y-2

Answer 2

So what is the next step you would do?

Answer 3

idk

Answer 4

So we want to get y by itself.
Lets add 2 to each side.

Answer 5

\[x+2 = \frac{ 1 }{ 3 }y\]

Answer 6

Does that make sense?

Answer 7

So how will we now "move" the 1/3?

Answer 8

Okay.
f(x)=1/3x-2

Take f(x) = y
y = 1/(3x - 2)
y*(3x - 2) = 1
3xy - 2y = 1
-1 - 2y= - 3xy
-(1 + 2y) = -3xy
1 + 2y = 3xy
(1 + 2y)/y = 3x
(1 + 2y)/3y = x

Lastly, replace y with x, we have:
(1 + 2x)/3x = y

Which is the inverse.

Answer 9

Wait, is it \[F(x) = \frac{ 1 }{ 3x - 2 }?\]

Answer 10

Or is it \[F(x) = \frac{ 1 }{ 3 }x - 2?\]

Answer 11

Wouldn't it be 3(x+2)=y
y=3x+6
\[f ^{-1}(x) = 3x+6\]

Answer 12

thats what i got but i got -3x but i see what i did wrong, thank you

Answer 13

Thank you.