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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