What is the range of y= x/(x^2+x-6) ?

The range of y= x/(x^2+x-6) is -infinity <f(x)<infinity

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range of y= x/(x^2+x-6)

range

y = \frac{x}{x ^{2} + x - 6}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{x}{x ^{2} + x - 6} = y

Multiply both sides by

x^{2} + x - 6

x = y (x^{2} + x - 6)

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

Discriminant

x = y (x^{2} + x - 6) : 25 y^{2} - 2 y + 1

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

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

in f l ec t i o n f (x) = x^{3} - 6 x^{2} - 36 x

in t erce pt s f (x) = y^{2} - x - 25 = 0

in v erse f (x) = 4 x + 16

y = - 3 x - 1

cr i t i c a l \frac{x ^{2} - 1}{x ^{3}}

What is the range of y= x/(x^2+x-6) ?
The range of y= x/(x^2+x-6) is -infinity <f(x)<infinity