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

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

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

range

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

f (x) < \frac{6}{5} or f (x) > \frac{6}{5}

Interval Notation

(- \infty, \frac{6}{5}) \cup (\frac{6}{5}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < \frac{6}{5} or f (x) > \frac{6}{5}

y = cos (2 x)

\frac{x + 7}{x ^{2} - 14 x + 49}

csc (0.1 x + 1.2)

∣ 3 ∣, - ∣ 4 ∣, - 2, 9

f (x) = x^{5} - 3 x^{3}

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