What is the range of x/(x^2-16) ?

The range of x/(x^2-16) is -infinity <f(x)<infinity

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

range of x/(x^2-16)

range

\frac{x}{x ^{2} - 16}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{x}{x ^{2} - 16} = y

Multiply both sides by

x^{2} - 16

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

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

Discriminant

x = y (x^{2} - 16) : 1 + 64 y^{2}

1 + 64 y^{2} \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

f (x) = ∣ x - 2 ∣

f (x) = \frac{3 x ^{2} + 2 x - 1}{6 x ^{2} - 7 x - 3}

f (x) = 2 x^{3} - 113

y = 2 x^{2} - 12 x - 2

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

What is the range of x/(x^2-16) ?
The range of x/(x^2-16) is -infinity <f(x)<infinity