What is the range of f(x)=\sqrt[3]{(x+1)/(x-1)} ?

The range of f(x)=\sqrt[3]{(x+1)/(x-1)} is f(x) 1

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range of f(x)=\sqrt[3]{(x+1)/(x-1)}

range

f (x) < 1 or f (x) > 1

Interval Notation

(- \infty, 1) \cup (1, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

Inverse of

\frac{1 + x ^{3}}{x ^{3} - 1}

Find the domain of each inverse function

Domain of

\frac{1 + x ^{3}}{x ^{3} - 1} : x < 1 or x > 1

Combine the intervals

f (x) < 1 or f (x) > 1

y = - 3 cos (2 x) - 2.5

f (x) = 3 (4)^{x}

e^{4 x}

x^{2} - 6 x + 4

f (x) = \frac{2 x + 2}{3 x - 4}

What is the range of f(x)=\sqrt[3]{(x+1)/(x-1)} ?
The range of f(x)=\sqrt[3]{(x+1)/(x-1)} is f(x)<1\lor f(x)>1