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Question
If f : R → R is given by f(x) = x3, write f−1 (1).
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Solution
Let f−1 (1) = x ... (1)
⇒ f(x)= 1
⇒ x3= 1
⇒ x3−1= 0
⇒ (x−1 (x2+ x + 1 ) = 0 [using the identity:a3−b3 ( a −b ) ( a2+ ab + b2) ]
⇒ x=1 ( as x ∈ R)
⇒ f−1 (1) = {1} [ from (1) ]
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