What is the range of 6/(x-5)+1 ?

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

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range of 6/(x-5)+1

range

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

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{6}{x - 5} + 1

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

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

f (x) = \frac{x ^{2} + 4 x}{- 4 x ^{2} + 36}

f (c) = \frac{9}{5} c + 32

(3, 8), (2, - 1)

f (x) = x^{3} + 3 x + 9

f (x) = \frac{5 x}{x ^{3} - 2 x}