What is the range of f(x)=(-4x+1)/(2x-3) ?

The range of f(x)=(-4x+1)/(2x-3) is f(x) -2

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range of f(x)=(-4x+1)/(2x-3)

range

f (x) = \frac{- 4 x + 1}{2 x - 3}

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{- 4 x + 1}{2 x - 3}

Inverse of

\frac{- 4 x + 1}{2 x - 3} : \frac{1 + 3 x}{2 ( 2 + x )}

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

What is the range of f(x)=(-4x+1)/(2x-3) ?
The range of f(x)=(-4x+1)/(2x-3) is f(x)<-2\lor f(x)>-2