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

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

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

range

\frac{4 x}{x - 1}

f (x) < 4 or f (x) > 4

Interval Notation

(- \infty, 4) \cup (4, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{4 x}{x - 1}

Inverse of

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

\frac{x}{x - 4}

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < 4 or f (x) > 4

f (x) = 4 x - 2

- x^{2} + 5 x - 7

Y (x) = \frac{2}{3} x + 3

- \frac{9}{2 t t}

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