What is the range of-2(x-1)^{1/3} ?

The range of-2(x-1)^{1/3} is -infinity <f(x)<infinity

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range of-2(x-1)^{1/3}

range

- 2 (x - 1)^{\frac{1}{3}}

- \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:

- 2 (x - 1)^{\frac{1}{3}}

Inverse of

- 2 (x - 1)^{\frac{1}{3}} : - \frac{x ^{3}}{8} + 1

- \frac{x ^{3}}{8} + 1

Find the domain of each inverse function

Domain of

- \frac{x ^{3}}{8} + 1 : - \infty < x < \infty

Combine the intervals

- \infty < f (x) < \infty

What is the range of-2(x-1)^{1/3} ?
The range of-2(x-1)^{1/3} is -infinity <f(x)<infinity