What is the range of f(x)=(10x+40)/(x-5) ?

The range of f(x)=(10x+40)/(x-5) is f(x) 10

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range of f(x)=(10x+40)/(x-5)

range

f (x) = \frac{10 x + 40}{x - 5}

f (x) < 10 or f (x) > 10

Interval Notation

(- \infty, 10) \cup (10, \infty)

Solution steps

The function range is the combined domain of the inverse functions

Find the inverse function(s) of:

\frac{10 x + 40}{x - 5}

Inverse of

\frac{10 x + 40}{x - 5} : \frac{40 + 5 x}{x - 10}

\frac{40 + 5 x}{x - 10}

Find the domain of each inverse function

Domain of

\frac{40 + 5 x}{x - 10} : x < 10 or x > 10

Combine the intervals

f (x) < 10 or f (x) > 10

f (x) = \frac{4 x}{x ^{2} - 1}

(1, - 9.5), (4, - 4.5)

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

\frac{x ^{2}}{6 x ^{2} + 4}

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

What is the range of f(x)=(10x+40)/(x-5) ?
The range of f(x)=(10x+40)/(x-5) is f(x)<10\lor f(x)>10