What is the range of (5x)/(2-x^2) ?

The range of (5x)/(2-x^2) is -infinity <f(x)<infinity

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range of (5x)/(2-x^2)

range

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

- \infty < f (x) < \infty

Interval Notation

(- \infty, \infty)

Solution steps

Rewrite as

\frac{5 x}{2 - x ^{2}} = y

Multiply both sides by

2 - x^{2}

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

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

Discriminant

5 x = y (2 - x^{2}) : 25 + 8 y^{2}

25 + 8 y^{2} \geq 0 :

True for all

y \in R

Therefore the range is

- \infty < f (x) < \infty

f (x) = - x^{3} + 3 x^{2} + 24 x + 1

y = - 3 cos (2 x) - 2.5

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

e^{4 x}

What is the range of (5x)/(2-x^2) ?
The range of (5x)/(2-x^2) is -infinity <f(x)<infinity