What is the range of 3\sqrt[3]{x} ?

The range of 3\sqrt[3]{x} is -infinity <f(x)<infinity

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range of 3\sqrt[3]{x}

range

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

Inverse of

\frac{x ^{3}}{27}

Find the domain of each inverse function

Domain of

\frac{x ^{3}}{27} : - \infty < x < \infty

Combine the intervals

- \infty < f (x) < \infty

3 - (x - 4)^{2}

f (x) = - x^{2} - x + 2

f (x) = \frac{5 x + 2}{x ^{2} + 6 x + 8}

f (x) = (x - 2)

f (x) = \frac{x ^{2} + 5 x + 4}{x ^{2} - 4}

What is the range of 3\sqrt[3]{x} ?
The range of 3\sqrt[3]{x} is -infinity <f(x)<infinity