How do you find #f^-1(x)# given #f(x)=1/x^3#?

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Answer 1 · 2016-11-23T12:20:23

The answer is #f^(-1)(x)=1/x^(1/3)#

Let #y=1/x^3#

Then, #x^3=1/y#

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

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

The verification is #f(f^(-1)(x))=x#

Let's do this

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