What is the range of f(x)=(10)/(x^2-4) ?

The range of f(x)=(10)/(x^2-4) is f(x) 0

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range of f(x)=(10)/(x^2-4)

range

f (x) = \frac{10}{x ^{2} - 4}

f (x) \leq - \frac{5}{2} or f (x) > 0

Interval Notation

(- \infty, - \frac{5}{2}] \cup (0, \infty)

Solution steps

Rewrite as

\frac{10}{x ^{2} - 4} = y

Multiply both sides by

x^{2} - 4

10 = y (x^{2} - 4)

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

Discriminant

10 = y (x^{2} - 4) : 16 y^{2} + 40 y

16 y^{2} + 40 y \geq 0 : y \leq - \frac{5}{2} or y \geq 0

Check if the range interval endpoints are included

y = - \frac{5}{2} :

Included

y = 0 :

Excluded

Therefore the range is

f (x) \leq - \frac{5}{2} or f (x) > 0

f (x) = 2 \frac{( x - 3 )}{4} + 1

\frac{3}{x}

f (x) = 2 - (x - 4.3) - 5.75

x^{2} - \frac{3}{5}

x^{3} + 11

What is the range of f(x)=(10)/(x^2-4) ?
The range of f(x)=(10)/(x^2-4) is f(x)<=-5/2 \lor f(x)>0