What is the range of (4x)/(9x-1) ?

The range of (4x)/(9x-1) is f(x) 4/9

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range of (4x)/(9x-1)

range

\frac{4 x}{9 x - 1}

f (x) < \frac{4}{9} or f (x) > \frac{4}{9}

Interval Notation

(- \infty, \frac{4}{9}) \cup (\frac{4}{9}, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{4 x}{9 x - 1}

Inverse of

\frac{4 x}{9 x - 1} : \frac{x}{9 x - 4}

\frac{x}{9 x - 4}

Find the domain of each inverse function

Domain of

\frac{x}{9 x - 4} : x < \frac{4}{9} or x > \frac{4}{9}

Combine the intervals

f (x) < \frac{4}{9} or f (x) > \frac{4}{9}

(1.2) (5.8)

sec^{2} (2 x) d x

y = x e^{- 2 x^{2}}

f (x) = \frac{1 + 3 x ^{2} - x ^{3}}{x ^{2}}

f (x) = \frac{( - 4 x ^{2} + 100 )}{5 x - 25}

What is the range of (4x)/(9x-1) ?
The range of (4x)/(9x-1) is f(x)< 4/9 \lor f(x)> 4/9