Question

find the inverse

Answer 1

\[f(x)=\frac{ x^2 }{ 3 }\]

Answer 2

Basic outline:

step 1) replace f(x) with y
step 2) swap x and y
step 3) solve for y

Answer 3

You'll have to restrict the domain so that the function is one-to-one. Otherwise, the inverse will not be a function.

Answer 4

One restriction you could make is \(\Large x \ge 0\)

Answer 5

okay so what do I do after I restrict it

Answer 6

follow that outline I posted

Answer 7

\[\Large f(x)=\frac{ x^2 }{ 3 }\]
\[\Large y=\frac{ x^2 }{ 3 }\]
\[\Large x=\frac{ y^2 }{ 3 }\]
solve for y. Keep in mind that \(\Large x \ge 0\)

Answer 8

Also, when x and y swap, everything about them swaps as well

So if \(\Large x \ge 0\) in the original, then \(\Large y \ge 0\) for the inverse

Answer 9

o should I square root the two sides?

Answer 10

before that, multiply both sides by 3

isolate the y^2 first, then isolate y itself

Answer 11

\[\sqrt{3x}=y\]

Answer 12

now idk what to do

Answer 13

so the inverse is \[\Large f^{-1}(x) = \sqrt{3x}\]
where \(\Large x \ge 0\)

Answer 14

so that's the answer?

Answer 15

like there isn't anything else to do to it?

Answer 16

what do mean "anything else to do to it" ?

once you get to sqrt(3x), you're done

Answer 17

okay

Answer 18

thanks for helping me again ;0

Answer 19

glad to be of help