If #f(x)=x^3-1# find the inverse #g(x)# of the function #f(x)#?

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Answer 1 · 2018-05-23T12:16:08

# g(x) = root(3)(x+1) #

We seek the inverse:

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

Let #y=f^(-1)(x) iff x=f(y)#, Then:

# x=y^3-1 #

And now we rearrange:

# y^3 = x+1 #

# :. y = root(3)(x+1) #

Hence, we have:

# g(x) = root(3)(x+1) #