What is the range of y=(-1)/(x-2)+3 ?

The range of y=(-1)/(x-2)+3 is f(x) 3

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range of y=(-1)/(x-2)+3

range

y = \frac{- 1}{x - 2} + 3

f (x) < 3 or f (x) > 3

Interval Notation

(- \infty, 3) \cup (3, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{- 1}{x - 2} + 3

Inverse of

\frac{- 1}{x - 2} + 3 : \frac{2 x - 7}{x - 3}

\frac{2 x - 7}{x - 3}

Find the domain of each inverse function

Domain of

\frac{2 x - 7}{x - 3} : x < 3 or x > 3

Combine the intervals

f (x) < 3 or f (x) > 3

f (x) = 7 x^{2} - 10

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

f (x) = \frac{4 x}{x - 3}

\frac{x ^{2} + 7 x + 12}{x ^{2} + x - 6}

f (x) = 100 - x^{2}

What is the range of y=(-1)/(x-2)+3 ?
The range of y=(-1)/(x-2)+3 is f(x)<3\lor f(x)>3