What is the domain of $f (x) = (4 \frac{x}{3}) ({(x^{2} - 1)}^{- \frac{1}{3}})$ $f(x) = (4x/3)((x^2 - 1)^(-1/3))$ ?

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Answer 1 · 2015-09-18T14:56:57

Refer to explanation

It should be $x^{2} - 1 > 0 \Rightarrow (x - 1) (x + 1) > 0$ $x^2-1>0=>(x-1)(x+1)>0$ hence the range is

$(- \infty, - 1) U (1, + \infty)$ $(-oo,-1)U(1,+oo)$

What is the domain of f(x)=(4x3)((x2−1)−13)f(x) = (4x/3)((x^2 - 1)^(-1/3))?