Question

Find the inverse of this function

Answer 1

can someone explain how to do this?

Answer 2

@Lowkey.S @Loli @babygirl4556

Answer 3

@imqwerty @zepdrix @.Sam. @Awolflover1

Answer 4

You have to solve the equation
\[y=\sqrt[3]{x-2}+8
\]
for x in terms of y

Answer 5

okay so what would be my first step after that? do I get rid of the square root? I am really having trouble

Answer 6

@eliesaab

Answer 7

\[y-8=\sqrt[3]{x-2}
\]

Answer 8

Cube both sides

Answer 9

\[y^3-8^3=x-2\]

Answer 10

\[
(y-8)^3=x-2
\]

Answer 11

is that right..? lol

Answer 12

No

Answer 13

okay and then where do you go next from that?

Answer 14

\[
y^3-24 y^2+192 y-512=x-2
\]

Answer 15

okay but how did you get there?

Answer 16

Use the formula
\[
(a-b)^3=a^3-3 a^2 b+3 a b^2-b^3
\]

Answer 17

okay and then after that do you just add the 2 to the other side to solve for x?

Answer 18

Yes

Answer 19

and then after that do you do anything else?

Answer 20

replace y by x to get the inverse function is
\[
g(x)=x^3-24 x^2+192 x-510
\]

Answer 21

thats not one of my answer choices :(

Answer 22

What are your answer choices?

Answer 23

It could be the same thing since here we expanded

Answer 24

f-1(x)=(x-8)^3+2
f-1(x)=(x+8)^3+2

Answer 25

i have two more let me type them

Answer 26

\[
(x-8)^3+2
\]

Answer 27

\[f^-1(x)=\sqrt[3]{x-8} +2\]

Answer 28

That is the same thing that I gave you where we expanded \((x-8)^3\)

Answer 29

The answer is \[
(x-8)^3 +2\]

Answer 30

okay thanks for your help

Answer 31

You are very welcome