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

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

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

range

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

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

Interval Notation

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

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

e x t re m e f (x) = x^{3} - 4 x^{2} - 16 x + 9

cr i t i c a l f (x) = 2 x - 4 x

d o main f (x) = x + (1 - x)

m o n o t o n e y = \frac{x ^{2}}{( x - 2 ) ^{2}}

s l o p e - 2 x - 1

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