What is the range of 1/(x^2) ?

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

range of 1/(x^2)

range

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

f (x) > 0

Interval Notation

(0, \infty)

Solution steps

Rewrite as

\frac{1}{x ^{2}} = y

Multiply both sides by

x^{2}

1 = y x^{2}

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

Discriminant

1 = y x^{2} : 4 y

4 y \geq 0 : y \geq 0

Check if the range interval endpoints are included

y = 0 :

Excluded

Therefore the range is

f (x) > 0