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Functions — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMathsFunctions2 Marks
Question
If f : R → R is given by f(x) = x3, write f-1(1).
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Answer

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 $(\text{as x}\in\text{R})$
⇒ f-1(1) = {1} [from (1)]

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