What is the range of (8x)/(9x-1) ?

The range of (8x)/(9x-1) is f(x) 8/9

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range of (8x)/(9x-1)

range

\frac{8 x}{9 x - 1}

f (x) < \frac{8}{9} or f (x) > \frac{8}{9}

Interval Notation

(- \infty, \frac{8}{9}) \cup (\frac{8}{9}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{8 x}{9 x - 1}

Inverse of

\frac{8 x}{9 x - 1} : \frac{x}{9 x - 8}

\frac{x}{9 x - 8}

Find the domain of each inverse function

Domain of

\frac{x}{9 x - 8} : x < \frac{8}{9} or x > \frac{8}{9}

Combine the intervals

f (x) < \frac{8}{9} or f (x) > \frac{8}{9}

f (x) = sin^{2} (x)

y = 1115 x + 1415

x^{4} - 4 x^{3} - 5 x^{2} + 16 x + 4

1 + (8 + x)^{\frac{1}{2}}

f (x) = 4 x^{3} - 6 x^{2} + 5 x - 2

What is the range of (8x)/(9x-1) ?
The range of (8x)/(9x-1) is f(x)< 8/9 \lor f(x)> 8/9