What is the range of-(7x)/(6x-5) ?

The range of-(7x)/(6x-5) is f(x) -7/6

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range of-(7x)/(6x-5)

range

- \frac{7 x}{6 x - 5}

f (x) < - \frac{7}{6} or f (x) > - \frac{7}{6}

Interval Notation

(- \infty, - \frac{7}{6}) \cup (- \frac{7}{6}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

- \frac{7 x}{6 x - 5}

Inverse of

- \frac{7 x}{6 x - 5} : \frac{5 x}{6 x + 7}

\frac{5 x}{6 x + 7}

Find the domain of each inverse function

Domain of

\frac{5 x}{6 x + 7} : x < - \frac{7}{6} or x > - \frac{7}{6}

Combine the intervals

f (x) < - \frac{7}{6} or f (x) > - \frac{7}{6}

f (x) = \frac{( x + 3 )}{x + 6}

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

f (x) = 4 x^{2} - 6

- 5 cos (\frac{x}{3} + \frac{π}{2}) - 4

(- 1, 3), (3, 5)

What is the range of-(7x)/(6x-5) ?
The range of-(7x)/(6x-5) is f(x)<-7/6 \lor f(x)>-7/6