What is the range of x/(7-x^2) ?

The range of x/(7-x^2) is -infinity <f(x)<infinity

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range of x/(7-x^2)

range

\frac{x}{7 - x ^{2}}

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{x}{7 - x ^{2}} = y

Multiply both sides by

7 - x^{2}

x = y (7 - x^{2})

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

Discriminant

x = y (7 - x^{2}) : 1 + 28 y^{2}

1 + 28 y^{2} \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

f (x) = \frac{- 2 x}{- 5 x + 4}

f (x) = x^{5} (x + 1) (x - 1)

\frac{x ^{2} - 3 x - 10}{x - 5}

f (x) = \frac{( x + 8 )}{x - 4}

- 2 x^{2} + 11

What is the range of x/(7-x^2) ?
The range of x/(7-x^2) is -infinity <f(x)<infinity