What is the range of f(x)=(x+6)/(2x-4) ?

The range of f(x)=(x+6)/(2x-4) is f(x) 1/2

range of f(x)=(x+6)/(2x-4)

range

f (x) = \frac{x + 6}{2 x - 4}

f (x) < \frac{1}{2} or f (x) > \frac{1}{2}

Interval Notation

(- \infty, \frac{1}{2}) \cup (\frac{1}{2}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x + 6}{2 x - 4}

Inverse of

\frac{x + 6}{2 x - 4} : \frac{6 + 4 x}{2 x - 1}

\frac{6 + 4 x}{2 x - 1}

Find the domain of each inverse function

Domain of

\frac{6 + 4 x}{2 x - 1} : x < \frac{1}{2} or x > \frac{1}{2}

Combine the intervals

f (x) < \frac{1}{2} or f (x) > \frac{1}{2}

e x t re m e f (x) = x^{3} - 3 x + 27

r an g e 3 sin (x)

e x t re m e f (x) = 1 - x

in t erce pt s f (x) = \frac{x + 1}{x ^{2} - 3 x - 4}

e x t re m e f (x) = 6 x^{2} + 1 - x

What is the range of f(x)=(x+6)/(2x-4) ?
The range of f(x)=(x+6)/(2x-4) is f(x)< 1/2 \lor f(x)> 1/2