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

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

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

range

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

f (x) < 5 or f (x) > 5

Interval Notation

(- \infty, 5) \cup (5, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{5 x}{x - 3}

Inverse of

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

\frac{3 x}{x - 5}

Find the domain of each inverse function

Domain of

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

Combine the intervals

f (x) < 5 or f (x) > 5

- x^{2} - 6 x

(0, 7), (1, 0)

f (x) = - 16 x^{2} + 40

2 x^{2} - 5 x + 1

(- 1, 3), (4, - 2)

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