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f-x-x-1-x-2-2-1-3-find-the-domain-of-f-




Question Number 141945 by Sammie last updated on 25/May/21
f(x)=(((∣x∣−1)(∣x∣−2)^2 ))^(1/3)   find the domain of f
$$\mathrm{f}\left(\mathrm{x}\right)=\sqrt[{\mathrm{3}}]{\left(\mid\mathrm{x}\mid−\mathrm{1}\right)\left(\mid\mathrm{x}\mid−\mathrm{2}\right)^{\mathrm{2}} } \\ $$$$\mathrm{find}\:\mathrm{the}\:\mathrm{domain}\:\mathrm{of}\:\mathrm{f} \\ $$
Answered by MJS_new last updated on 25/May/21
if we use ((−t))^(1/3) =−(t)^(1/3)  ∀t∈R^+ ⇒ f(x) is defined ∀x∈R
$$\mathrm{if}\:\mathrm{we}\:\mathrm{use}\:\sqrt[{\mathrm{3}}]{−{t}}=−\sqrt[{\mathrm{3}}]{{t}}\:\forall{t}\in\mathbb{R}^{+} \Rightarrow\:{f}\left({x}\right)\:\mathrm{is}\:\mathrm{defined}\:\forall{x}\in\mathbb{R} \\ $$

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