Question

What is the inverse function of
f(n)=2(n-2)^3?

Answer 1

[f^{-1}(n) = sqrt[3]{n/2} + 2

Explanation:

To find the inverse function of \(f(n) = 2(n-2)^3\), let's start by expressing \(n\) in terms of \(f(n)\) and then solving for \(n\).

\[f(n) = 2(n-2)^3\]

First, isolate the term with \(n\):

\[f(n)/2 = (n-2)^3\]

Now, take the cube root of both sides to solve for \(n-2\):

\[(n-2) = \sqrt[3]{f(n)/2}\]

Finally, solve for \(n\):

\[n = \sqrt[3]{f(n)/2} + 2\]

So, the inverse function of \(f(n) = 2(n-2)^3\) is:

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