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

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

range of 8/(x^2-100)

range

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

Interval Notation

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

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