What is the range of f(x)=(60)/(x(x+4)) ?

The range of f(x)=(60)/(x(x+4)) is f(x) 0

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range of f(x)=(60)/(x(x+4))

range

f (x) = \frac{60}{x ( x + 4 )}

f (x) \leq - 15 or f (x) > 0

Interval Notation

(- \infty, - 15] \cup (0, \infty)

Solution steps

Rewrite as

\frac{60}{x ( x + 4 )} = y

Multiply both sides by

x (x + 4)

60 = y x (x + 4)

The range is the set of y for which the discriminant is greater or equal to zero

Discriminant

60 = y x (x + 4) : 16 y^{2} + 240 y

16 y^{2} + 240 y \geq 0 : y \leq - 15 or y \geq 0

Check if the range interval endpoints are included

y = - 15 :

Included

y = 0 :

Excluded

Therefore the range is

f (x) \leq - 15 or f (x) > 0

\frac{5 ^{x}}{5 ^{x} + 3 ^{x}}

f (x) = \frac{4}{x + 3} + 2

\frac{e ^{x}}{x}

3 sin (x)

f (x) = \frac{5}{x - 9}

What is the range of f(x)=(60)/(x(x+4)) ?
The range of f(x)=(60)/(x(x+4)) is f(x)<=-15\lor f(x)>0