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

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

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

range

f (x) = \frac{8 x}{9 x - 1}

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

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}

x - 4

\frac{x ^{2} + x + 1}{x ^{2} - x + 1}

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

\frac{1}{x ^{2} - 10 x + 15}

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

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