What is the range of (x-1)/(25-x^2) ?

The range of (x-1)/(25-x^2) 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-1)/(25-x^2)

range

\frac{x - 1}{25 - x ^{2}}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{x - 1}{25 - x ^{2}} = y

Multiply both sides by

25 - x^{2}

x - 1 = y (25 - x^{2})

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

Discriminant

x - 1 = y (25 - x^{2}) : 1 + 100 y^{2} + 4 y

1 + 100 y^{2} + 4 y \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

f (x) = \frac{1}{2 9 - x}

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

11 x + 6 y = 3

f (x) = x^{2} + 9 x

- \frac{1 - cos ( 4 x )}{1 + cos ( 4 x )}

What is the range of (x-1)/(25-x^2) ?
The range of (x-1)/(25-x^2) is -infinity <f(x)<infinity