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

The range of f(x)= x/(6-x) is f(x) -1

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range of f(x)= x/(6-x)

range

f (x) = \frac{x}{6 - x}

f (x) < - 1 or f (x) > - 1

Interval Notation

(- \infty, - 1) \cup (- 1, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{x}{6 - x}

Inverse of

\frac{x}{6 - x} : \frac{6 x}{x + 1}

\frac{6 x}{x + 1}

Find the domain of each inverse function

Domain of

\frac{6 x}{x + 1} : x < - 1 or x > - 1

Combine the intervals

f (x) < - 1 or f (x) > - 1

y = cos (x - \frac{π}{2})

f (x) = - 2 x^{4} + 7 x^{2}

\frac{x + 4}{2 x}

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

f (x) = \frac{x - 8}{5 x ^{2}}

What is the range of f(x)= x/(6-x) ?
The range of f(x)= x/(6-x) is f(x)<-1\lor f(x)>-1