What is the range of (3x+8)/(2x-3) ?

The range of (3x+8)/(2x-3) is f(x) 3/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

range of (3x+8)/(2x-3)

range

\frac{3 x + 8}{2 x - 3}

f (x) < \frac{3}{2} or f (x) > \frac{3}{2}

Interval Notation

(- \infty, \frac{3}{2}) \cup (\frac{3}{2}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{3 x + 8}{2 x - 3}

Inverse of

\frac{3 x + 8}{2 x - 3} : \frac{8 + 3 x}{2 x - 3}

\frac{8 + 3 x}{2 x - 3}

Find the domain of each inverse function

Domain of

\frac{8 + 3 x}{2 x - 3} : x < \frac{3}{2} or x > \frac{3}{2}

Combine the intervals

f (x) < \frac{3}{2} or f (x) > \frac{3}{2}

f (x) = \frac{x + 5}{x ^{2}}

f (x) = \frac{( 8 - 2 x )}{x + 3}

f (x) = \frac{x}{2 x + 5}

f (x) = x + 10

What is the range of (3x+8)/(2x-3) ?
The range of (3x+8)/(2x-3) is f(x)< 3/2 \lor f(x)> 3/2