What is the range of \sqrt[3]{x+5} ?

The range of \sqrt[3]{x+5} is -infinity <f(x)<infinity

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range of \sqrt[3]{x+5}

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

x^{3} - 5

Find the domain of each inverse function

Domain of

x^{3} - 5 : - \infty < x < \infty

Combine the intervals

- \infty < f (x) < \infty

f (x) = 3 x^{2} + 9

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

4 \cdot (\frac{2}{3})^{x} + 1

f (x) = \frac{1}{4} x

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

What is the range of \sqrt[3]{x+5} ?
The range of \sqrt[3]{x+5} is -infinity <f(x)<infinity