For the function f(x)=(x-3)^3+1 find f^-1(x) ?

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Answer 1 · 2018-01-08T08:24:58

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

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

or

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

To find the inverse function #f^-1(x)#, we arrange the equation in terms of #x#.

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

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

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

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

So, the inverse of #f(x)=(x-3)^3+1# is

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