What is the range of 1/(x-4)+2 ?

The range of 1/(x-4)+2 is f(x) 2

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range of 1/(x-4)+2

range

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

f (x) < 2 or f (x) > 2

Interval Notation

(- \infty, 2) \cup (2, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

\frac{1}{x - 4} + 2 : \frac{4 x - 7}{x - 2}

\frac{4 x - 7}{x - 2}

Find the domain of each inverse function

Domain of

\frac{4 x - 7}{x - 2} : x < 2 or x > 2

Combine the intervals

f (x) < 2 or f (x) > 2

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

f (x) = \frac{1}{6 x + 4}

(1, - 1), (9, 4)

3 x^{2} + 6 x - 1

12 x + 3 y = 7