What is the range of (2+x)/(x^2(1-x)) ?

The range of (2+x)/(x^2(1-x)) is -infinity <f(x)<infinity

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range of (2+x)/(x^2(1-x))

range

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

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

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

Domain of

\frac{2 + x}{x ^{2} ( 1 - x )} : x < 0 or 0 < x < 1 or x > 1

Extreme Points of

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

Minimum

(\frac{- 5 - 57}{4}, \frac{143 - 19 57}{16}),

Minimum

(\frac{- 5 + 57}{4}, \frac{143 + 19 57}{16})

Find the range for the interval

- \infty < x < 0 : \frac{143 - 19 57}{16} \leq f (x) < \infty

Find the range for the interval

0 < x < 1 : \frac{143 + 19 57}{16} \leq f (x) < \infty

Find the range for the interval

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

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

f (x) \geq \frac{143 - 19 57}{16} or f (x) \geq \frac{143 + 19 57}{16} or f (x) < 0

- \infty < f (x) < \infty

f (x) = 2 x^{3} - 24 x - 6

f (t) = t^{4} - \frac{2}{3} t^{6}

f (x) = 7 sin (x)

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

f (x) = 3 + 1

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