What is the range of (x-1)/(x^2-4) ?

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

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range of (x-1)/(x^2-4)

range

\frac{x - 1}{x ^{2} - 4}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{x - 1}{x ^{2} - 4} = y

Multiply both sides by

x^{2} - 4

x - 1 = y (x^{2} - 4)

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

Discriminant

x - 1 = y (x^{2} - 4) : 1 + 16 y^{2} - 4 y

1 + 16 y^{2} - 4 y \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

f (x) = x^{2} - 7 x + 10

f (x) = \frac{4 - x}{x ^{2} - 3 x}

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

(x^{2} - 1)^{\frac{2}{3}}

4 x + 2 y = 7

What is the range of (x-1)/(x^2-4) ?
The range of (x-1)/(x^2-4) is -infinity <f(x)<infinity