Question

how do you find the inverse of f(x):
f(x)=2/3x+6

Answer 1

It's a 4 step process

Answer 2

First, replace f(x) with "y"

Answer 3

\[f(x)=\frac{2}{3}x+6\] or
\[f(x)=\frac{2}{3x+6}\]

Answer 4

So you've got
f(x) = 2/3x+6

y = 2/3x + 6

Next, the "x" and "y" switch places.

Answer 5

So you've got:

x = 2/3y +6

Next, you solve for "y"

Answer 6

x=2/3y+6

Subtract 6 from both sides

x-6 = 2/3y

Then, you can multiply by 3/2 on both sides, and you'll have that y by itself.

3/2(x-6) = y

Answer 7

And the last step is to replace y with:
\[ f^{-1}(x)\]

Answer 8

So you're left with:
\[f^{-1}(x)=\frac{3(x-6)}{2}\]

Answer 9

Or, if you'd prefer:
\[ f^{-1}(x)=\frac{3}{2}x - 9\]