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

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

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

range

\frac{3 x}{2 - x}

f (x) < - 3 or f (x) > - 3

Interval Notation

(- \infty, - 3) \cup (- 3, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{3 x}{2 - x}

Inverse of

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

\frac{2 x}{x + 3}

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < - 3 or f (x) > - 3

f (x) = \frac{4 x}{x + 5}

f (x) = 2 - x^{6} - x^{8}

f (x) = 8 - 2 x

y = 6 cos (2 x + \frac{π}{2})

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