What is the range of f(x)=(x^2)/(x+2) ?

The range of f(x)=(x^2)/(x+2) is f(x) = 0

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

range of f(x)=(x^2)/(x+2)

range

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

f (x) \leq - 8 or f (x) \geq 0

Interval Notation

(- \infty, - 8] \cup [0, \infty)

Solution steps

Rewrite as

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

Multiply both sides by

x + 2

x^{2} = y (x + 2)

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

Discriminant

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

y^{2} + 8 y \geq 0 : y \leq - 8 or y \geq 0

Check if the range interval endpoints are included

y = - 8 :

Included

y = 0 :

Included

Therefore the range is

f (x) \leq - 8 or f (x) \geq 0

f (x) = 4^{x + 2}

f (x) = 5 - 4 x

g (x) = \frac{2 x}{x ^{2} - 36}

2^{x - 5} - 11

f (x) = - \frac{1}{7} x - \frac{2}{7}

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