What is the range of (3+4x)/(1-5x) ?

The range of (3+4x)/(1-5x) is f(x) -4/5

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range of (3+4x)/(1-5x)

range

\frac{3 + 4 x}{1 - 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{3 + 4 x}{1 - 5 x}

Inverse of

\frac{3 + 4 x}{1 - 5 x} : - \frac{3 - x}{4 + 5 x}

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

Find the domain of each inverse function

Domain of

- \frac{3 - 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}

f (x) = \frac{( 5 x - 1 )}{( - 1 + 5 x )}

y = x^{2} - 2 x - 24

f (x) = x^{2} + x - 12

f (x) = 2 x + 7

f (x) = x^{3} - x^{2} - 9 x + 9

What is the range of (3+4x)/(1-5x) ?
The range of (3+4x)/(1-5x) is f(x)<-4/5 \lor f(x)>-4/5