What is the range of f(x)=(x^3)/(x^4) ?

The range of f(x)=(x^3)/(x^4) is f(x) 0

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range of f(x)=(x^3)/(x^4)

range

f (x) = \frac{x ^{3}}{x ^{4}}

f (x) < 0 or f (x) > 0

Interval Notation

(- \infty, 0) \cup (0, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x ^{3}}{x ^{4}}

Inverse of

\frac{x ^{3}}{x ^{4}} : \frac{1}{x}

\frac{1}{x}

Find the domain of each inverse function

Domain of

\frac{1}{x} : x < 0 or x > 0

Combine the intervals

f (x) < 0 or f (x) > 0

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

\frac{1}{2 x + 4}

f (x) = (\frac{x - 2}{7})^{\frac{1}{3}}

f (x) = 36 x + \frac{9}{x}

f (x) = \frac{1}{x ^{2} - x - 90}

What is the range of f(x)=(x^3)/(x^4) ?
The range of f(x)=(x^3)/(x^4) is f(x)<0\lor f(x)>0