Let `C` denote the set of all complex numbers. A function `f: C->C` is defined by `f(x)=x^3` . Write `f^(-1)(1)` .

Explanation

Let `f^{-1}(1)=x quad cdots(1)`



`Rightarrow {f}({x})=1`


`Rightarrow {x}^{3}=1 ldots ldots ldots ldots ldots[text { Given }] `


`Rightarrow({x}-1)({x}^{2}+{x}+1)=0 quad text { [Since, } {a}^{3}-{b}^{3}=({a}-{b})({a}^{2}+{ab}+{b}^{2}) text { ] }`



After solving `x^{2}+x+1=0`, we get `x=frac{1 pm sqrt{3} i}{2}`


Let, `w=frac{1 pm sqrt{3} i}{2}`


...