What is the range of 8/(x^2-100) ?

The range of 8/(x^2-100) is f(x) 0

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range of 8/(x^2-100)

range

\frac{8}{x ^{2} - 100}

f (x) \leq - \frac{2}{25} or f (x) > 0

Interval Notation

(- \infty, - \frac{2}{25}] \cup (0, \infty)

Solution steps

Rewrite as

\frac{8}{x ^{2} - 100} = y

Multiply both sides by

- x^{2} + 100

- 8 = y (- x^{2} + 100)

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

Discriminant

- 8 = y (- x^{2} + 100) : 4 y (100 y + 8)

4 y (100 y + 8) \geq 0 : y \leq - \frac{2}{25} or y \geq 0

Check if the range interval endpoints are included

y = - \frac{2}{25} :

Included

y = 0 :

Excluded

Therefore the range is

f (x) \leq - \frac{2}{25} or f (x) > 0

f (x) = x + 3

f (x) = 12 x^{2} - x^{3}

f (x) = - 16 x^{2} + 64 x + 80

x^{4} - 3 x^{2} - 4

\frac{x ^{2}}{x ^{2} - 1}

What is the range of 8/(x^2-100) ?
The range of 8/(x^2-100) is f(x)<=-2/25 \lor f(x)>0