How do you find the inverse of #f(x)=root3x#?

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Answer 1 · 2017-05-30T17:42:00

#f^(- 1)(x) = x^(3)#

We have: #f(x) = root(3)(x)#

Let's replace #f(x)# with #y#:

#Rightarrow y = root(3)(x)#

Interchanging variables:

#Rightarrow x = root(3)(y)#

We must now solve the equation for #y#:.

Cubing both sides of the equation:

#Rightarrow (x)^(3) = (root(3)(y))^(3)#

#Rightarrow x^(3) = y#

#Rightarrow y = x^(3)#

Now, let's replace #y# with #f^(- 1)(x)#:

#therefore f^(- 1)(x) = x^(3)#