What is the range of f(x)=(4x-3)/(6-5x) ?

The range of f(x)=(4x-3)/(6-5x) is f(x) -4/5

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range of f(x)=(4x-3)/(6-5x)

range

f (x) = \frac{4 x - 3}{6 - 5 x}

f (x) < - \frac{4}{5} or f (x) > - \frac{4}{5}

Interval Notation

(- \infty, - \frac{4}{5}) \cup (- \frac{4}{5}, \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 - 5 x}

Inverse of

\frac{4 x - 3}{6 - 5 x} : - \frac{- 3 - 6 x}{4 + 5 x}

- \frac{- 3 - 6 x}{4 + 5 x}

Find the domain of each inverse function

Domain of

- \frac{- 3 - 6 x}{4 + 5 x} : x < - \frac{4}{5} or x > - \frac{4}{5}

Combine the intervals

f (x) < - \frac{4}{5} or f (x) > - \frac{4}{5}

(3, - 2), (3, 2)

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

f (x) = 5^{x} - 4

f (x) = \frac{1 - 7 x}{1 + 4 x}

m = - 1, (- 0.5, 1.5)

What is the range of f(x)=(4x-3)/(6-5x) ?
The range of f(x)=(4x-3)/(6-5x) is f(x)<-4/5 \lor f(x)>-4/5