What is the range of \sqrt[3]{x}-4 ?

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

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range of \sqrt[3]{x}-4

range

3 x - 4

- \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:

3 x - 4

Inverse of

3 x - 4 : x^{3} + 12 x^{2} + 48 x + 64

x^{3} + 12 x^{2} + 48 x + 64

Find the domain of each inverse function

Domain of

x^{3} + 12 x^{2} + 48 x + 64 : - \infty < x < \infty

Combine the intervals

- \infty < f (x) < \infty

e x t re m e f (x) = - x^{2}

d o main f (x) = 2^{x - 3}

cr i t i c a l f (x) = 9 - x^{2}

cr i t i c a l \frac{1}{x ^{2} - 1}

a sy m pt o t es f (x) = \frac{x ^{2} + x - 2}{2 x ^{2} + 1}

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