What is the range of f(x)=(2x-5)/(x-3) ?

The range of f(x)=(2x-5)/(x-3) is f(x) 2

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range of f(x)=(2x-5)/(x-3)

range

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

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{2 x - 5}{x - 3}

Inverse of

\frac{2 x - 5}{x - 3} : \frac{- 5 + 3 x}{x - 2}

\frac{- 5 + 3 x}{x - 2}

Find the domain of each inverse function

Domain of

\frac{- 5 + 3 x}{x - 2} : x < 2 or x > 2

Combine the intervals

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

f (x) = \frac{4 x}{4 x - 5}

f (x) = (x - 13)^{2}

f (x) = (x^{3} + 2)^{3} + 2

y = 7^{x}

x^{4} - 4 x^{3} - x^{2} + 14 x + 10

What is the range of f(x)=(2x-5)/(x-3) ?
The range of f(x)=(2x-5)/(x-3) is f(x)<2\lor f(x)>2