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

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

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

range

f (x) = \frac{( 1 - x )}{( 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{1 - x}{2 x - 1}

Inverse of

\frac{1 - x}{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}

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