Question

Fan and medal reward
Which function is the inverse of f(x)=x^3−6x^2+12x−8?

Answer 1

f^(-1) (x) = x^(1\/3)+2

Answer 2

is it
\[f^-1(x)=\sqrt[3]{x}+2\]
or
\[f^-1(x)=\sqrt[3]{x+2}\]
@Famous5

Answer 3

@dmndlife24

Answer 4

f(x)=x^3−6x^2+12x−8

that function is the same as...

f(x)=(x-2)^3

Now to find the inverse just interchange the x and y variables and solve for y...
(first change f(x) to y)

y=(x-2)^3

Interchange...

x=(y-2)^3

Now solve for y to find that it is equivalent to

\[y = \sqrt[3]{x+2}\]

Answer 5

Lastly, just substitute back in the "f-1(x)"

Answer 6

thank you so much! @dmndlife24

Answer 7

No problem