Question

Find f^-1 for the function f(x)=^3sqrt x-2 +8.
A)f^-1(x)=(x-8)^3+2
B)f^-1(x)=(x+8)^3+2
C)f^-1(x)=^3sqrt x-8 +2
D)f^-1(x)=(x-8)^3-2

Answer 1

Well, I am here.

Answer 2

The original function is ??
It is not clearly typed!

Answer 3

One minute please

Answer 4

I am sorry for late!

Answer 5

If your problem looks like that:

\[y=\sqrt[3]{x-2}+8\], we will proceed as follows;;;

Answer 6

Firstly, we will solve for x; i.e. separate x-terms in one side and the other terms at the other side.

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

Secondly: swap x and y; just exchange their positions
\[(x-8)^3+2=y\]
\[y=(x-8)^3+2\]
\[f^{-1}(x)=(x-8)^3+2\]

So your choice would be the first one (A)

Answer 7

Hope that helps

Answer 8

what is the question ?

Answer 9

i dont know if 3mar did it right or not

Answer 10

does this
f(x)=^3sqrt x-2 +8. A)f^-1(x)=(x-8)^3+2

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

Answer 11

yes

Answer 12

3mar shows the steps. you first add -8 to both sides
then "cube" both sides
then add +2 to both sides
you get
(y-8)^3 + 2 = x
then swap letters
y= (x-8)^3 + 2
or, if you like
\[ f^{-1}(x) = (x-8)^3 + 2 \]