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

The range of (x^2)/(x^2-4) is f(x) 1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

range of (x^2)/(x^2-4)

range

\frac{x ^{2}}{x ^{2} - 4}

f (x) \leq 0 or f (x) > 1

Interval Notation

(- \infty, 0] \cup (1, \infty)

Solution steps

Rewrite as

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

Multiply both sides by

x^{2} - 4

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

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

Discriminant

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

16 y^{2} - 16 y \geq 0 : y \leq 0 or y \geq 1

Check if the range interval endpoints are included

y = 0 :

Included

y = 1 :

Excluded

Therefore the range is

f (x) \leq 0 or f (x) > 1

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

f (x) = 3 x e^{8 x}

f (x) = - \frac{9 sin ( x )}{4 x ^{2} - 9 sin ( x )}

2 + 2 x

5^{x - 2} + 4

What is the range of (x^2)/(x^2-4) ?
The range of (x^2)/(x^2-4) is f(x)<= 0\lor f(x)>1