Question

Find the inverse of \(f(x) = x^\frac{1}{n}\)

Answer 1

In the lecture notes, my teacher wrote \(f􀀀^{-1}(x) = x^n\), but isn't
\(f^{-1}(f(x)) = (x^\frac{1}{n})^n = x^1 = x \ne 1\)?

Answer 2

re-write f(x) as y.
switch the x and the y,
and then solve for y after you switched x and y.

Answer 3

Please read my comment above

Answer 4

and then once you find that; which is the inverse function, write the notation \(\large\color{black}{ f^{-1}(x) }\).

\(\large\color{black}{ f(x)=x^{1/n} }\) \(\LARGE\color{white}{ \rm \left| \right| }\)
\(\large\color{black}{ y=x^{1/n} }\) \(\LARGE\color{white}{ \rm \left| \right| }\)
\(\large\color{black}{ x=y^{1/n} }\) \(\LARGE\color{white}{ \rm \left| \right| }\)
\(\large\color{black}{ x^n=y }\) \(\LARGE\color{white}{ \rm \left| \right| }\)
\(\large\color{black}{ f^{-1}(x)=x^n }\) \(\LARGE\color{white}{ \rm \left| \right| }\)

Answer 5

this is all you need to do here.

Answer 6

I know how to find inverse of a function (the steps), I just misunderstood something

Answer 7

and include your restriction that: \(\large\color{black}{ x\ne1 }\) as the \(\large\color{black}{ f(x) }\) requires you.

Answer 8

Inverse of a function => \(f^{-1}(f(x)) = x\)
Inverse of a number => \(f^{-1}(f(c)) = 1\)

Answer 9

I would think so........