What is the range of 8/((2x-5)^3) ?

The range of 8/((2x-5)^3) is f(x) 0

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range of 8/((2x-5)^3)

range

\frac{8}{( 2 x - 5 ) ^{3}}

f (x) < 0 or f (x) > 0

Interval Notation

(- \infty, 0) \cup (0, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{8}{( 2 x - 5 ) ^{3}}

Inverse of

\frac{8}{( 2 x - 5 ) ^{3}} : \frac{2 x ^{\frac{2}{3}} + 5 x}{2 x}

\frac{2 x ^{\frac{2}{3}} + 5 x}{2 x}

Find the domain of each inverse function

Domain of

\frac{2 x ^{\frac{2}{3}} + 5 x}{2 x} : x < 0 or x > 0

Combine the intervals

f (x) < 0 or f (x) > 0

What is the range of 8/((2x-5)^3) ?
The range of 8/((2x-5)^3) is f(x)<0\lor f(x)>0