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

The range of (x^3+2x)/x is f(x)>2

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

range

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

f (x) > 2

Solution steps

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

Domain of

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

Simplify

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

Extreme Points of

x^{2} + 2 :

Minimum

(0, 2)

Find the range for the interval

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

Find the range for the interval

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

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

f (x) > 2 or f (x) > 2

f (x) > 2

\frac{x}{x ^{2} + 15 x + 54}

(- 6.2) (- 6.6)

f (x) = 5 x - 1

f (x) = - x^{3} + 9 x^{2} - 8 x - 4

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