What is the range of f(x)=(3x^2)/(x^2-9) ?

The range of f(x)=(3x^2)/(x^2-9) is f(x) 3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

range of f(x)=(3x^2)/(x^2-9)

range

f (x) = \frac{3 x ^{2}}{x ^{2} - 9}

f (x) \leq 0 or f (x) > 3

Interval Notation

(- \infty, 0] \cup (3, \infty)

Solution steps

Rewrite as

\frac{3 x ^{2}}{x ^{2} - 9} = y

Multiply both sides by

x^{2} - 9

3 x^{2} = y (x^{2} - 9)

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

Discriminant

3 x^{2} = y (x^{2} - 9) : 36 y^{2} - 108 y

36 y^{2} - 108 y \geq 0 : y \leq 0 or y \geq 3

Check if the range interval endpoints are included

y = 0 :

Included

y = 3 :

Excluded

Therefore the range is

f (x) \leq 0 or f (x) > 3

f (x) = x + 9

y = - x^{2} - 1

f (x) = 6 sin (\frac{1}{3}) x

f (x) = x^{4} - 3

11 q + 5 \leq 49

What is the range of f(x)=(3x^2)/(x^2-9) ?
The range of f(x)=(3x^2)/(x^2-9) is f(x)<= 0\lor f(x)>3