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

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

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

range

\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}

2 lo g_{2} (x) + 6

f (x) = 2 x + 3

f (x) = \frac{x ^{2} - 3}{5}

x^{2} + 12 x + 11

f (x) = x^{3} + 4 x

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