What is the range of (x-7)/(12x+2) ?

The range of (x-7)/(12x+2) is f(x) 1/12

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range of (x-7)/(12x+2)

range

\frac{x - 7}{12 x + 2}

f (x) < \frac{1}{12} or f (x) > \frac{1}{12}

Interval Notation

(- \infty, \frac{1}{12}) \cup (\frac{1}{12}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x - 7}{12 x + 2}

Inverse of

\frac{x - 7}{12 x + 2} : \frac{- 7 - 2 x}{12 x - 1}

\frac{- 7 - 2 x}{12 x - 1}

Find the domain of each inverse function

Domain of

\frac{- 7 - 2 x}{12 x - 1} : x < \frac{1}{12} or x > \frac{1}{12}

Combine the intervals

f (x) < \frac{1}{12} or f (x) > \frac{1}{12}

\frac{x + 2}{x ^{3} - 3}

y = 3 x + 12

(- 3, - 4), (0, - 3)

f (x) = \frac{x}{7 x + 36}

\frac{( x ^{3} + 6 x ^{2} + 9 x )}{x + 3}

What is the range of (x-7)/(12x+2) ?
The range of (x-7)/(12x+2) is f(x)< 1/12 \lor f(x)> 1/12