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

The range of x/(x^2-9) is -infinity <f(x)<infinity

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range of x/(x^2-9)

range

\frac{x}{x ^{2} - 9}

- \infty < f (x) < \infty

Solution steps

Rewrite as

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

Multiply both sides by

x^{2} - 9

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

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

Discriminant

x = y (x^{2} - 9) : 1 + 36 y^{2}

1 + 36 y^{2} \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

f (x) = (x - 1)^{2}

f (x) = 2 x + 8

x^{2} - 5 x + 6

x^{2} - 3 x - 4

f (x) = 7 x^{3} - 4

What is the range of x/(x^2-9) ?
The range of x/(x^2-9) is -infinity <f(x)<infinity