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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

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

range

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

f (x) < \frac{1}{4} or f (x) > \frac{1}{4}

Interval Notation

(- \infty, \frac{1}{4}) \cup (\frac{1}{4}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x}{4 x - 5}

Inverse of

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

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

Find the domain of each inverse function

Domain of

\frac{5 x}{4 x - 1} : x < \frac{1}{4} or x > \frac{1}{4}

Combine the intervals

f (x) < \frac{1}{4} or f (x) > \frac{1}{4}

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