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

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

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

range

f (x) = \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) = 1 + \frac{3}{x} + \frac{2}{x ^{2}}

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

2 x + 3 y = - 12

\frac{5}{x} + 6

f (v) = (2 v - 7)^{2}

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