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

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

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

range

\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

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

y = \frac{3}{4} - 2 - x

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

f (x) = sin (x), 0 \leq x < π^{2}

\frac{- x ^{2} - x + 6}{x ^{2} + 3 x - 4}

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