How do you find the domain and range of the inverse of the given function f(x) = x^3?

1 Answer
Tiago Hands
Apr 17, 2015

Step 1. Let's find the inverse function of the given function.

y=x^3

x=y^(1/3)

:. f^-1(x)=root(3)x

Step 2. Now let's take a look at the graph of f^-1(x)=root(3)x

What we can see below is the fact that x can be an element of a real number (xERR - which is the domain of this inverse function), and that f^-1(x) can also be an element of a real number
(f^-1(x)ERR - which is the range of this inverse function).

graph{y=root(3)x [-10, 10, -5, 5]}

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