What is the range of (2x+3)/(x-4) ?

The range of (2x+3)/(x-4) is f(x) 2

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range of (2x+3)/(x-4)

range

\frac{2 x + 3}{x - 4}

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 + 3}{x - 4}

Inverse of

\frac{2 x + 3}{x - 4} : \frac{3 + 4 x}{x - 2}

\frac{3 + 4 x}{x - 2}

Find the domain of each inverse function

Domain of

\frac{3 + 4 x}{x - 2} : x < 2 or x > 2

Combine the intervals

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

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

f (x) = - 4 (x - 2)^{2} + 16

f (x) = ln (\frac{x}{x + 2})

f (x) = 2 x^{2} - 8 x - 3

\frac{3}{4} x + 7

What is the range of (2x+3)/(x-4) ?
The range of (2x+3)/(x-4) is f(x)<2\lor f(x)>2