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

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

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

range

f (x) = \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

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