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

The range of (2x^2)/((x+2)(x-3)) is f(x) = 48/25

Popular >

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

range

\frac{2 x ^{2}}{( x + 2 ) ( x - 3 )}

f (x) \leq 0 or f (x) \geq \frac{48}{25}

Interval Notation

(- \infty, 0] \cup [\frac{48}{25}, \infty)

Solution steps

Rewrite as

\frac{2 x ^{2}}{( x + 2 ) ( x - 3 )} = y

Multiply both sides by

(x + 2) (x - 3)

2 x^{2} = y (x + 2) (x - 3)

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

Discriminant

2 x^{2} = y (x + 2) (x - 3) : 25 y^{2} - 48 y

25 y^{2} - 48 y \geq 0 : y \leq 0 or y \geq \frac{48}{25}

Check if the range interval endpoints are included

y = 0 :

Included

y = \frac{48}{25} :

Included

Therefore the range is

f (x) \leq 0 or f (x) \geq \frac{48}{25}

f (x) = \frac{1}{x ^{2} - 5 x + 4}

f (x) = \frac{6 e ^{x}}{e ^{x} - 9}

f (x) = x^{2} - 4

f (x) = (3) lo g_{5} (7 x - 4)

x^{2} - 5 x + 6

What is the range of (2x^2)/((x+2)(x-3)) ?
The range of (2x^2)/((x+2)(x-3)) is f(x)<= 0\lor f(x)>= 48/25