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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

range

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}

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