What is the range of (6x+7)/(5x-6) ?

The range of (6x+7)/(5x-6) is f(x) 6/5

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

range of (6x+7)/(5x-6)

range

\frac{6 x + 7}{5 x - 6}

f (x) < \frac{6}{5} or f (x) > \frac{6}{5}

Interval Notation

(- \infty, \frac{6}{5}) \cup (\frac{6}{5}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{6 x + 7}{5 x - 6}

Inverse of

\frac{6 x + 7}{5 x - 6} : \frac{7 + 6 x}{5 x - 6}

\frac{7 + 6 x}{5 x - 6}

Find the domain of each inverse function

Domain of

\frac{7 + 6 x}{5 x - 6} : x < \frac{6}{5} or x > \frac{6}{5}

Combine the intervals

f (x) < \frac{6}{5} or f (x) > \frac{6}{5}

What is the range of (6x+7)/(5x-6) ?
The range of (6x+7)/(5x-6) is f(x)< 6/5 \lor f(x)> 6/5