What is the range of f(x)=((4x-3))/((6-2x)) ?

The range of f(x)=((4x-3))/((6-2x)) is f(x) -2

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range of f(x)=((4x-3))/((6-2x))

range

f (x) = \frac{( 4 x - 3 )}{( 6 - 2 x )}

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 - 3}{6 - 2 x}

Inverse of

\frac{4 x - 3}{6 - 2 x} : - \frac{- 3 - 6 x}{2 ( 2 + x )}

- \frac{- 3 - 6 x}{2 ( 2 + x )}

Find the domain of each inverse function

Domain of

- \frac{- 3 - 6 x}{2 ( 2 + x )} : x < - 2 or x > - 2

Combine the intervals

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

(3, 6), (9, - 2)

\frac{- 5 x}{3 x + 5}

y = \frac{( 5 x - 3 )}{2 x + 6}

ln (x)

x^{4} + x^{3}

What is the range of f(x)=((4x-3))/((6-2x)) ?
The range of f(x)=((4x-3))/((6-2x)) is f(x)<-2\lor f(x)>-2