What is the range of (x-2)/(x^3+x) ?

The range of (x-2)/(x^3+x) is -infinity <f(x)<infinity

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range of (x-2)/(x^3+x)

range

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

- \infty < f (x) < \infty

Solution steps

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

Domain of

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

Extreme Points of

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

Maximum

(3.10380 \dots, 0.03344 \dots)

Find the range for the interval

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

Find the range for the interval

0 < x < \infty : - \infty < f (x) \leq 0.03344 \dots

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

f (x) > 0 or f (x) \leq 0.03344 \dots

- \infty < f (x) < \infty

f (x) = \frac{5}{x ^{2} - 49}

f (x) = \frac{( x + 19 )}{( x - 17 )}

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

f (x) = (x - 4)^{2} - 5

y = (x - 2)^{2}

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