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

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

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

range

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

f (x) < 4 or f (x) > 4

Interval Notation

(- \infty, 4) \cup (4, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

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

Inverse of

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

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

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < 4 or f (x) > 4

f (x) = (x - 3) e^{- x}

16 x - 48 - 3

\frac{4 x + 3}{2 x + 5}

f (x) = x^{3} - 6 x^{2} + 9 x + 5

\frac{x ^{2} - 6 x + 8}{x ^{2} - 16}

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