Question

Find the inverse of the function.
f(x)=3 cube rt (x/7) -9

Answer 1

\(\large\color{black}{ \displaystyle f(x)=3\sqrt[3]{\frac{x}{7}}-9 }\) like this?

Answer 2

\[f(x)= \sqrt[3]{x/7}-9\]

Answer 3

oh, so then
f(x)=cube rt (x/7) - 9

Answer 4

\(\large\color{black}{ \displaystyle f(x)=\sqrt[3]{\frac{x}{7}}-9 }\)

Answer 5

yeah

Answer 6

Steps:

`1. For convenience replace f(x) with y`
(y and f(x) are same thing, just for further manipulations)

`2. Switch x and y.`
(put x instead of y, and put y instead of x)

`3. In new equation, isolate the y.`

Answer 7

(you will then re-write \({\rm f}^{-1}(x)\) instead of y, after step 3, to denote that it is an inverse function)

Answer 8

ok, can you do step 1 for me please?

here is the code I am using, if you want
`\(\large\color{black}{ \displaystyle f(x)=3\sqrt[3]{\frac{x}{7}}-9 }\)`

Answer 9

\[x=\sqrt[3]{y/7} -9\]

Answer 10

very good, now isolate the y.

Answer 11

idk y but your code wasn't working

Answer 12

it should be, if you just put in text (not equation editor)

`\(\large\color{black}{ \displaystyle f(x)=\sqrt[3]{\frac{x}{7}}-9 }\)`
gives me
\(\large\color{black}{ \displaystyle f(x)=\sqrt[3]{\frac{x}{7}}-9 }\)

Answer 13

\(\large\color{black}{ \displaystyle x=\sqrt[3]{\frac{y}{7}}-9 }\)

Answer 14

obtained by:
`\(\large\color{black}{ \displaystyle x=\sqrt[3]{\frac{y}{7}}-9 }\)`

Answer 15

just copy paste, and put in your a reply. You can modify the code too.

Answer 16

I mean it is fine the way you are doing with equation editor too.

Answer 17

y=7x^3+189x^2+1701x+5103
that's what I got when I solved for y

Answer 18

but it's not one of my answer choices

Answer 19

\(\large\color{black}{ \displaystyle x=\sqrt[3]{\frac{y}{7}}-9 }\)

steps to isolate the y:

\(\rm 1.~~~~Add~~9~~to~~both~~sides.\)
\(\rm 2.~~~~Raise~~both~~sides~~to~~the~~3rd~~power.\)

your answer is correct

Answer 20

can I see the options, though?

Answer 21

yes, you didn't need to expand;)

Answer 22

leave it as it is, after you raised both sides to the 3rd power, multiply times 7 on both sides, and you are done.

Answer 23

\(\large\color{black}{ \displaystyle x+9=\sqrt[3]{x/7} }\)

\(\large\color{black}{ \displaystyle (x+9)^3=\left(\sqrt[3]{x/7}~\right)^3 }\)

\(\large\color{black}{ \displaystyle (x+9)^{3}=\left(\sqrt[\cancel{3}]{x/7}~\right)^{\cancel{3}} }\)

\(\large\color{black}{ \displaystyle (x+9)^3=x/7 }\)

and then final step to multiply both sides times 7.

Answer 24

hope this is making sense:)

Answer 25

oh ok thanks so much so it would be that last one

Answer 26

yup, that is option D. :D

Answer 27

which simplifies to D^2

Answer 28

jk