Question

may someone please help me on how to find the inverse for the problem I am about to post on the comments. Thanks

Answer 1

\[f(x)=\sqrt[5]{x-3}\]

Answer 2

substitute y for f(x)

Answer 3

okay

Answer 4

what do you have now?

Answer 5

\[y=\sqrt[5]{x-3}\]

Answer 6

Now, switch x and y (hint: they trade places)

Answer 7

\[x=\sqrt[5]{y-3}\]

Answer 8

Now, we want to strip the right side to the point of "y" being alone.

Answer 9

so do we add 3?

Answer 10

to begin, we need to get rid of the square root of 5. Do you know how to get rid of it on the right side, and bring it to the left side?

Answer 11

nope

Answer 12

we want to start with the outer layers first, since we can't add 3 yet.

Answer 13

ok

Answer 14

to get rid of square root of 5, u want to multiply it on both sides. Multiplying a square root with a square root cancels out.

Answer 15

okay

Answer 16

what do we multiply it by though?

Answer 17

5?

Answer 18

\[\sqrt[5]{x}=y-3\]

Answer 19

Do you understand how to get that part?

Answer 20

not really. How do we know what number to multiply it by?

Answer 21

@myininaya do you know whats "it" called when u multiply the square root to eliminate \[\sqrt[5]{y-3}\] that makes \[\sqrt[5]{}\]. I forgot what it is called.

Answer 22

\[\sqrt[5]{x}\]

Answer 23

isn't it to square both sides?

Answer 24

I think that is what it is called.

Answer 25

ok

Answer 26

Then, since were one step away from solving the inverse problem. Now you add 3 to the left side, and that is your answer.

Answer 27

Your answer should be \[y=\sqrt[5]{x}+3\]

Answer 28

oh okay thank you so much

Answer 29

You understand why we don't include "+3" in the square root?

Answer 30

A slight mistake, people could make.

Answer 31

wait why can't we include add 3 in the square root?

Answer 32

I think you meant to raise both sides to the 5th power earlier

Answer 33

\[x=\sqrt[5]{y-3} \\ x^5=y-3\]

Answer 34

Looking at the original equation, 3 is "packaged" together with the "x." Since, we have stripped the outer layer, the square root, \[\sqrt[5]{y-3}\] simply becomes y-3 (since we squared both sides, x becoming \[\sqrt[5]{x}\]

Answer 35

then last step add 3 on both sides

Answer 36

so then the answer would be \[x^5+3 \]

Answer 37

Oops, myininaya is correct. Sorry, I should of done this problem before typing it out. Haha :)

Answer 38

That's okay (:

Answer 39

but the same case still applies, once you strip the outer layer (square root etc) the 3 becomes free from the y and doesn't become a package with the "y."

Answer 40

okay thanks guys.