What is the range of (x+1)/(2x+1) ?

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

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range of (x+1)/(2x+1)

range

\frac{x + 1}{2 x + 1}

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 + 1}{2 x + 1}

Inverse of

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

\frac{1 - x}{2 x - 1}

Find the domain of each inverse function

Domain of

\frac{1 - 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}

f (x) = \frac{6 x}{sin ( x )}

f (x) = \frac{x + 3}{x ^{2} - 4}

f (x) = 4 (x - 3)^{5}

f (x) = 2 x^{2} - 8 x, x \geq 2

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

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