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Question

Let C denote the set of all complex numbers. A function f:CC is defined by f(x)=x3. Write f1(1).

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Solution

Let f1(1)=x ---- ( 1 )
f(x)=1
x3=1 ................... [ Given ]
(x1)(x2+x+1)=0 [ Since, a3b3=(ab)(a2+ab+b2) ]

After solving x2+x+1=0, we get x=1±3i2

Let, w=1±3i2

(x1)(xw)(xw2)=0
x=1,w,w2 [ As xC ]

From ( 1 ),
f1(1)={1,w,w2}

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