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

The range of (x^2-2x-3)/x is -infinity <f(x)<infinity

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range of (x^2-2x-3)/x

range

\frac{x ^{2} - 2 x - 3}{x}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

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

Multiply both sides by

x

x^{2} - 2 x - 3 = y x

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

Discriminant

x^{2} - 2 x - 3 = y x : y^{2} + 4 y + 16

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

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

What is the range of (x^2-2x-3)/x ?
The range of (x^2-2x-3)/x is -infinity <f(x)<infinity