For the function #f(x)=(x-3)^3+1#, how do you find #f^-1(x)#?

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For the function #f(x)=(x-3)^3+1#, how do you find #f^-1(x)#?

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Answer 1 · 2017-02-28T21:37:06

In order to find for any function #f(x)#, we must apply the 'transformation' #y=x#. In order to do that, we must define #x# in terms of #y#, ie., find #f(y)#, then set #y=x#.

Let #y=f(x)#

#y=(x-3)^3+1#

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

#x-3=root(3)(y-1)#

#x=3+root(3)(y-1)#

We've now found #f(y)#, so we must set #y=x# by replacing #x# with #y# and #y# with #x#.

#f^-1(x)=y=3+root(3)(x-1)#

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For the function #f(x)=(x-3)^3+1#, how do you find #f^-1(x)#?

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