What is the range of (x(2x^2-3x+1))/(x^3+1) ?

The range of (x(2x^2-3x+1))/(x^3+1) is f(x) 2

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range of (x(2x^2-3x+1))/(x^3+1)

range

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

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

Interval Notation

(- \infty, 2) \cup (2, \infty)

Solution steps

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

Domain of

\frac{x ( 2 x ^{2} - 3 x + 1 )}{x ^{3} + 1} : x < - 1 or x > - 1

Extreme Points of

\frac{x ( 2 x ^{2} - 3 x + 1 )}{x ^{3} + 1} :

Maximum

(0.20778 \dots, 0.09534 \dots),

Minimum

(0.75412 \dots, - 0.06595 \dots)

Find the range for the interval

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

Find the range for the interval

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

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

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

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

y = x + 1

f (x) = \frac{x + 2}{x}

f (x) = arctan (ln (e^{t a n (x^{2})}))

y = \frac{1}{2} x - 4

What is the range of (x(2x^2-3x+1))/(x^3+1) ?
The range of (x(2x^2-3x+1))/(x^3+1) is f(x)<2\lor f(x)>2