RELATIONS AND FUNCTIONS — Maths STD 12 Science — Question
Gujarat BoardEnglish MediumSTD 12 ScienceMathsRELATIONS AND FUNCTIONS2 Marks
Question
If f : C → C is defined by f(x) = (x - 2)3, write f-1(-1).
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Answer
Let f-1(1) = x ......(1) ⇒ f(x) = -1 ⇒ (x - 2)3 = -1 $\Rightarrow\ \text{x}-2=-1\ \text{or }-\omega\text{ or }-\omega^2$ as the roots of $(-1)^\frac{1}{3}$ are $-1,-\omega\text{ and }-\omega^2,$ where $\omega=\frac{1\pm\text{i}\sqrt{3}}{2}$ $\Rightarrow\ \text{x}=-1+2\text{ or }2-\omega\text{ or }2-\omega^2=1,2-\omega,2-\omega$ $\Rightarrow\ \text{f}^{-1}(-1)=1,2-\omega,2-\omega^2$ [from 1]
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