Find the domain of the function f(x)=sqrt[n]{x^{2}-1}, when n is odd.

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Step:1 ：Rearrange the inequality to (x^{2} >= 1).Step:2 ：Take the square root of both sides to get (|x| >= 1).Step:3 ：Solve for x. The absolute value inequality (|x| >= 1) has two solutions: (x >= 1) and (x <= -1).Step:4 ：(boxed{(-infty, -1] cup [1, infty)}) is the domain of the function (f(x) = sqrt[n]{x^{2}-1}), when n is odd.

Answer

Step: 1 ：Rearrange the inequality to (x^{2} >= 1).Step: 2 ：Take the square root of both sides to get (|x| >= 1).Step: 3 ：Solve for x. The absolute value inequality (|x| >= 1) has two solutions: (x >= 1) and (x <= -1).Step: 4 ：(boxed{(-infty, -1] cup [1, infty)}) is the domain of the function (f(x) = sqrt[n]{x^{2}-1}), when n is odd.

Find the domain of the function f(x)=\sqrt[n]{x^{2}-1}, when n is odd.

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