What is the range of f(x)= x/(-8x+3) ?

The range of f(x)= x/(-8x+3) is f(x) -1/8

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range of f(x)= x/(-8x+3)

range

f (x) = \frac{x}{- 8 x + 3}

f (x) < - \frac{1}{8} or f (x) > - \frac{1}{8}

Interval Notation

(- \infty, - \frac{1}{8}) \cup (- \frac{1}{8}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x}{- 8 x + 3}

Inverse of

\frac{x}{- 8 x + 3} : \frac{3 x}{8 x + 1}

\frac{3 x}{8 x + 1}

Find the domain of each inverse function

Domain of

\frac{3 x}{8 x + 1} : x < - \frac{1}{8} or x > - \frac{1}{8}

Combine the intervals

f (x) < - \frac{1}{8} or f (x) > - \frac{1}{8}

What is the range of f(x)= x/(-8x+3) ?
The range of f(x)= x/(-8x+3) is f(x)<-1/8 \lor f(x)>-1/8