What is the range of f(x)=\sqrt[3]{x+4} ?

The range of f(x)=\sqrt[3]{x+4} is -infinity <f(x)<infinity

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range of f(x)=\sqrt[3]{x+4}

range

- \infty < f (x) < \infty

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

Inverse of

x^{3} - 4

Find the domain of each inverse function

Domain of

x^{3} - 4 : - \infty < x < \infty

Combine the intervals

- \infty < f (x) < \infty

f (x) = - x^{3} - 3 x^{2}

x^{2} - 6 x - y + 11 = 0

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

- 5 x + 4 y = 0

f (x) = \frac{10 x + 40}{x - 5}

What is the range of f(x)=\sqrt[3]{x+4} ?
The range of f(x)=\sqrt[3]{x+4} is -infinity <f(x)<infinity