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

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

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range of (4x)/(x^3-4x)

range

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

f (x) < - 1 or f (x) > 0

Interval Notation

(- \infty, - 1) \cup (0, \infty)

Solution steps

Find the minimum and maximum value in each defined interval and unite the results

Domain of

\frac{4 x}{x ^{3} - 4 x} : x < - 2 or - 2 < x < 0 or 0 < x < 2 or x > 2

Simplify

\frac{4 x}{x ^{3} - 4 x} : \frac{4}{x ^{2} - 4}

Extreme Points of

\frac{4}{x ^{2} - 4} :

Maximum

(0, - 1)

Find the range for the interval

- \infty < x < - 2 : 0 < f (x) < \infty

Find the range for the interval

- 2 < x < 0 : - \infty < f (x) < - 1

Find the range for the interval

0 < x < 2 : - \infty < f (x) < - 1

Find the range for the interval

2 < x < \infty : 0 < f (x) < \infty

Combine the ranges of all domain intervals to obtain the function range

f (x) > 0 or f (x) < - 1 or f (x) < - 1 or f (x) > 0

f (x) < - 1 or f (x) > 0

2 x - y + 4 = 0

f (x) = x + 1 - \frac{7 - x}{x}

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

\frac{1 - 4 x}{2 + x}

(13, 2), (7, 10)

What is the range of (4x)/(x^3-4x) ?
The range of (4x)/(x^3-4x) is f(x)<-1\lor f(x)>0