What is the range of f(x)=(x+6)/(x-5) ?

The range of f(x)=(x+6)/(x-5) is f(x) 1

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range of f(x)=(x+6)/(x-5)

range

f (x) = \frac{x + 6}{x - 5}

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 - 5}

Inverse of

\frac{x + 6}{x - 5} : \frac{6 + 5 x}{x - 1}

\frac{6 + 5 x}{x - 1}

Find the domain of each inverse function

Domain of

\frac{6 + 5 x}{x - 1} : x < 1 or x > 1

Combine the intervals

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

f (x) = \frac{( x + 3 ) ^{\frac{1}{4}}}{9}

3 x - y + y

f (x) = - y^{2}

f (x) = \frac{3}{x ^{2} - 81}

f (x) = lo g_{3} (x) + 6

What is the range of f(x)=(x+6)/(x-5) ?
The range of f(x)=(x+6)/(x-5) is f(x)<1\lor f(x)>1