What is the range of 2/(x-6)+4 ?

The range of 2/(x-6)+4 is f(x) 4

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range of 2/(x-6)+4

range

\frac{2}{x - 6} + 4

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

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{2}{x - 6} + 4

Inverse of

\frac{2}{x - 6} + 4 : \frac{6 x - 22}{x - 4}

\frac{6 x - 22}{x - 4}

Find the domain of each inverse function

Domain of

\frac{6 x - 22}{x - 4} : x < 4 or x > 4

Combine the intervals

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

(x + 3)^{2} - 1

- \frac{1}{2} x^{4} + 48 x^{2}

y = \frac{1}{4} x + 9, at (2 - 2)

f (x) = \frac{( - 4 x ^{2} - 2 x + 1 )}{2 x + 3}

f (x) = \frac{1}{2 x - 8}