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Question

If f:RR is given by f(x)=x3, write f1(1).

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Solution

f:RR is given by f(x)=x3.

Let f1(1)=x ---- ( 1 )
f(x)=1
x3=1 ...................[ Given ]
x31=0
(x1)(x2+x+1)=0 ...................[ Since, a3b3=(a+b)(a2+ab+b2) ]

Value of x of x2+x+1 will be complex number.

As xR, then x2+x+1=0 is not possible.
x1=0
x=1
From ( 1 ),
f1(1)={1}

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